Molar heat capacity measurement of CaHCl and CaHBr

Article abstract of DOI:10.1007/s12039-019-1675-9

Abstract: Molar heat capacities of two hydride ion conductors, namely, CaHCl and CaHBr, were measured by differential scanning calorimetry. The measured molar heat capacity data of these compounds as a function of temperature is given by the following expressions:C_p < CaHCl > (J K^?1 mol^?1) = 57.806 + 16.420 × 10^?3.T ? 1.006 × 10⁶.T^?2C_p < CaHBr > (J K^?1 mol^?1) = 56.534 + 44.880 × 10^?3.T ? 1.481 × 10⁶.T^?2From the above expressions, molar enthalpy increments, entropies and Gibbs energy functions of these compounds were derived and reported. Graphic abstract: SYNOPSIS CaHCl and CaHBr are hydride ion conducting solid electrolytes find application in electrochemical hydrogen meter to determine dissolved hydrogen concentration in liquid sodium. Heat capacity of CaHCl and CaHBr were measured using DSC and reported.[Figure not available: see fulltext.]

Full text of DOI:10.1007/s12039-019-1675-9

J. Chem. Sci.
( 20 19 ) 1 31 :1 00
Ó In di an Aca dem y of Sc i en c es
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REGULAR ARTICLE
Special Issue on Ma t er ia ls C he mi str y
Molar heat capacity measurement of CaHCl and CaHBr
a
S S HYAM KUM AR , SAJ AL GHOS H , MANJ ULATA S AHU a nd R AJES H GANES AN
a
b
a ,
*
a
M at er ia ls Ch e m is t ry an d Me tal F ue l C ycl e Gr oup, In di ra Gan dhi C ent re fo r At om i c R es ear ch, Ho mi Bh a bh a
Na t io n al I ns t it ut e, K alp ak ka m 60 3 102 , Tam i l nad u, In di a
b
R ad i och em is t ry an d I s oto pe G r ou p, B habha At om i c R es earc h C e nt re, Mum b ai 400 085 , Mah aras ht r a, I nd i a
E- ma i l: r aj es h @i gc ar .g ov .in
MS r ecei v ed 7 M ay 2 01 9 ; r ev i s ed 2 5 J u ly 2 0 1 9; accep t ed 2 1 A u g u st 2 0 1 9
Abstract. Mo l ar he at ca pac iti es of t wo hyd ri de i on con duc t ors , nam el y, C aHC l and C aHB r , wer e me a su r ed
b y d i ff er en ti al s ca nn in g ca lor im e tr y . The m eas ur ed m ol ar hea t cap ac i ty dat a of t hes e com p ound s as a f un ct i o n
o f t em per at ur e is gi ve n by th e f ol lowi ng exp res s i ons :
-
1
-1
-3
6
-2
-2
C \ Ca HC l [ ( J K m ol ) = 57 .8 06 ? 16. 42 0 9 10 . T - 1. 006 9 10 . T
p
(3 08– 7 4 8 K)
(3 23– 7 1 3 K)
p
-
1
-1
-3
6
C \ Ca HB r [ ( J K m ol ) = 56 .53 4 ? 44. 88 0 9 10 . T - 1. 481 9 10 . T
Fr o m th e ab ov e ex pr es s i on s , m ol ar ent h al py i ncre m ent s , ent ro pi es and Gi bbs ene rgy fu nct i ons o f t he s e
c o mp o un ds w er e de ri ve d an d r epo r te d.
Keywords. Liq ui d s od i um ; hy dr o g en s ens o r; hyd ri de i on con duc t in g el e ct rol yt e; m ol ar hea t ca pa ci t y ;
d i ffe r ent ia l s ca nn in g ca lor i m et ry .
1
. Introduction
f or onl ine m onit or ing of th e c onc e ntr a ti on of hy dr oge n
in li qui d sod ium . A m ixt ur e of a lka li ne e ar t h hydr id es
a lon g wit h a lka li ne e ar t h ha li de s is e mp loye d a s the
Fa st b re e d e r re a ct o rs u se l iq ui d so di u m as th e he a t
t ra ns f e r me d i u m i n b ot h pr i mar y an d se co nd ar y c ool -
a n t c irc u i ts b e c a u s e o f i ts f avo r abl e ph y si cal , ch e mi ca l
2– 4
3
e le ct r oly te f or th is pur p ose .
C aC l –C a H a nd
2 2
5
C aB r –C a H pse ud o- bin ar y sys te ms we r e id e ntifi e d
2
2
1
a n d n u c le a r p ro p er t ie s. At t he st e am ge ne ra t or m od-
a s th er m odyn am i ca lly st ab le sys te ms f or th e de ve l-
opm e nt of suc h a n e le ct r oly te . I n th es e sys te ms , the
c om poun ds C aHC l a nd C aHB r a re th e hyd rid e ion
c ondu ct or s. I t is im por t an t to de te r mi ne th e t he r mo-
dyn am ic da ta of th es e c om poun ds. Thi s pa pe r r e por ts
th e m ea sur e m en t of m ola r he a t c ap ac it y da ta of C a HC l
a nd C aHB r f or th e te m pe ra t ur e r an ge 308 –74 8 K by
usi ng a di ff e r en tia l sc a nnin g c al or im et er .
u l e , li q u id s o d iu m an d wat e r ar e se pa ra te d by f er r it ic
t u b es o f 3 to 4 mm wal l t hi ck ne ss f or he at t ra nsf e r . All
p o s s ib le c a re is ta ke n t o av oi d di r ec t co nt a ct be twe e n
wa te r a n d s o d iu m as i n t he ev en t of an y mi cr o- cr a ck in
t h e fe rri ti c tu b e s , t he hi g h- t emp er at u re an d hi gh-
p re s s u re s te a m c an l ea k i nt o l iq ui d so di u m. As th e
re a c ti o n b e tw ee n so di u m an d wat e r i s hi ghly
e x o th er mi c, a n d th e r eac t io n pr o du ct s hy d ro ge n a nd
s o d iu m h y d ro x id e ar e ex pl o si ve an d ca us ti c , r es pe c-
t i v e ly , wo u l d c a u se f ur th er da ma ge. Hen ce , i t sho uld 2. Experimental
b e d e te c te d a t it s i nc ep ti o n st a ge f or q ui ck r em e dia l
2
.1 Preparation and characterization of samples
a ct i o n. It is a s a fe t y r equ i re men t f or on l in e mo n ito ri ng
h y d ro g e n a n d o x y g en co nc en tr at i o n i n l iq ui d sod ium
t o a v o id th i s ty p e o f ac ci de nt a l co nd i ti on .
A h y d ro g e n se ns or h as be en d eve l op ed in th e
a u t ho rs ’ la b o ra t o ry t o d et ect h ydr o gen co nc en tr a ti on a t
p p b le v e l s in li q u i d so di u m. I t i s es se nt i al ly a sol id
e l ec tr o ly te b a s e d el e ct ro ch em ic al co nc en tr at i on c el l
1
M o s t o f t h e c h e m i c a l s u s e d i n t h i s w o r k a r e a i r a n d
m o i s t u r e s e n s i t i v e a n d h e n c e w e r e h a n d l e d i n a r g o n
a t m o s p h e r e g l o v e b o x e s . H i g h p u r i t y i n e r t a t m o -
s p h e r e i s m a i n t a i n e d i n t h e g l o v e b o x e s u s i n g a
l i q u i d s o d i u m t r a y w h i c h g e t t e r s t r a c e l e v e l s o f
o x y g e n a n d m o i s t u r e (\1 p p m ) . C a H C l w a s p r e -
p a r e d b y h e a t i n g a s t o i c h i o m e t r i c m i x t u r e o f C a a n d
*
F o r co rr e sp on den ce

1
0 0 Pa g e 2 o f 7
J. Chem. Sci.
( 201 9) 13 1: 100
C a C l 2 i n t h e h y d r o g e n a t m o s p h e r e . C a C l 2 ( A R v e s s e l w a s t r a n s f e r r e d i n s i d e t h e g l o v e b o x a f t e r t h e
g r a d e , M / s . A B C R , G e r m a n y ) w a s p u r i fi e d b y u s u a l e v a c u a t i o n s t e p s . T h e s a l t w a s c a r e f u l l y s e p -
h e a t i n g a b o v e i t s m e l t i n g p o i n t a n d b y b u b b l i n g a r a t e d f r o m t h e q u a r t z c r u c i b l e i n s i d e t h e g l o v e b o x
a r g o n g a s s a t u r a t e d w i t h H C l v a p o r i n t h e m o l t e n a n d w a s s t o r e d i n s i d e a v e s s e l , e q u i p p e d w i t h K F -
s a l t . T h e e x p e r i m e n t a l s e t u p i s s h o w n s c h e m a t i c a l l y c o u p l i n g c l o s u r e , a s s e c o n d a r y c o n t a i n m e n t . T h e
i n F i g u r e 1 . D e t a i l s o f t h e p u r i fi c a t i o n p r o c e d u r e a r e p u r i t y o f t h e p r e p a r e d s a l t w a s a s c e r t a i n e d f r o m i t s
6
d e s c r i b e d e l s e w h e r e . C o m m e r c i a l g r a d e a r g o n g a s m e l t i n g p o i n t . A b o u t 2 0 m g o f t h e s a m p l e w a s t a k e n
([9 9 . 9 9 % , B h o r u k a G a s e s , I n d i a ) w a s b u b b l e d i n i n s i d e a t h i n w a l l e d 1 5 m m l o n g i r o n c r u c i b l e o f
H C l s o l u t i o n ( 3 7 % s o l u t i o n , E . M e r c k , I n d i a ) a n d 3 m m d i a m e t e r a n d h e r m e t i c a l l y s e a l e d u s i n g a
s u b s e q u e n t l y t h r o u g h o f P O ([9 8 % , R F C L I n d i a p u l s e d a r c w e l d i n g u n i t i n t h e g l o v e b o x . T h e
2
5
P v t . L t d . , I n d i a ) a n d C a C l ([9 7 % , H i m e d i a L a b o - m e l t i n g p o i n t w a s d e t e r m i n e d u s i n g t h e D T A
2
r a t o r i e s P v t . L t d . , I n d i a ) p o w d e r s p a c k e d ꢀUꢀ t u b e e q u i p m e n t , S E T S Y S 1 6 - 1 8 E v o l u t i o n ( M / s . S e t a r a m ,
c o l u m n s t o r e m o v e t h e m o i s t u r e . T h e d r y H C l - a r g o n F r a n c e ) . P r i o r t o t h e m e a s u r e m e n t , t e m p e r a t u r e
g a s m i x t u r e w a s b u b b l e d i n t h e m o l t e n C a C l f o r c a l i b r a t i o n o f D T A w a s c a r r i e d o u t b y m e a s u r i n g
2
3
s e v e r a l s t a g e s o f C a C l a n d P O p a c k e d c o l u m n s . The pu ri fie d C aC l wa s m ixe d wit h th e stoi ch io-
0 m i n . T h e o u t l e t g a s w a s t h e n p a s s e d t h r o u g h t h e m e l t i n g p o i n t s o f h i g h p u r i t y m e t a l s t a n d a r d s .
2
2
5
2
T h e s e c o l u m n s w e r e p r o v i d e d a t t h e o u t l e t t o m et ri c a mo unt of c al ci um m et al ( 99.5 % pur e , J ohns on
e l i m i n a t e t h e p o s s i b i l i t y o f i n g r e s s o f a i r / m o i s t u r e Ma t the y, Ge r ma ny) a nd he a te d in a hyd r oge n a tmo-
t h r o u g h b a c k s u c t i o n . F i n a l l y , t h e g a s w a s l e t o u t b y sph er e a t 750 °C f or 120 h. The sc he ma t ic of the
p a s s i n g t h r o u g h a N a O H ([9 7 % , E . M e r c k , I n d i a ) e xpe r im en ta l a sse m bly is sho wn in F igu re 2. A one
s c r u b b e r . T h e p r o c e s s w a s c o n t i n u e d f o r a n o t h e r e nd c los ed pu re ir on th im ble wit h a th in- wa ll e d por -
3 0 m i n , w i t h p u r e a r g o n g a s t o r e m o v e a n y t r a c e ti on a t th e bo ttom we lde d to a st ai nle ss st ee l pipe ,
l e v e l s o f H C l p r e s e n t i n t h e m e l t . T h e q u a r t z v e s s e l whi ch in tu rn is we lde d to a kn if e- e dge d fl an ge w as
a s s e m b l y c o n t a i n i n g t h e c r u c i b l e w i t h p u r i fi e d s a l t use d to ho ld C a, C aC l m ixt ur e a nd c los ed a t th e top. I t
2
w a s p l a c e d i n s i d e t h e t r a n s f e r p o r t o f t h e a r g o n wa s th en pl ac e d ove r a kn if e- e dge d fl an ge d sta inl es s
a t m o s p h e r e s o d i u m g l o v e b o x ( o x y g e n a n d m o i s t u r e st ee l ve sse l wit h pr ov isio n f or fl owin g hy dr oge n ga s
c o n t e n t \1 p p m ) w i t h a fl o w o f a r g o n m a i n t a i n e d a nd se a le d usi ng a c oppe r ga ske t. The hy dr oge n ga s
t h r o u g h t h e v e s s e l . D u r i n g t h i s t r a n s f e r , t h e q u a r t z di ff us ed th ro ugh th e th in ir on m em br a ne . The c a lc ium
v e s s e l w a s a t h i g h t e m p e r a t u r e ( *4 0 0 °C ) . A r g o n m et al wa s fi rs t c onve r te d to C aH in si tu a nd r e a ct ed
2
fl o w t h r o u g h t h e v e s s e l i s t h e n d i s c o n n e c t e d , a n d t h e wit h C aC l to pr od uce C aHC l.
2
Figure 1. S che m ati c di ag ram of t he s al t pur i fica t i on s et up.

J. Chem. Sci.
(2 01 9) 1 31 :1 00
P age 3 of 7
10 0
The qua nt ity of sa m ple s use d va r ie d f r om 25 to 40 mg.
The sa m ple s we r e ta ke n out of th e gl ove box mom e nt
be f or e lo ad ing in to th e in str um e nt. DS C m ea sur e me nts
we r e c ar r ie d ou t in th e te m pe ra t ur e r an ge of
-
1
3
1
08 –74 8 K usi ng 10 K m in
%H –Ar ga s m ixt ur e a s a pu rg e ga s wit h a fl ow r a te
he a tin g r ate w ith
2
-1
of 50 m L m in . A th re e - se gme nt he a tin g pr ogr a m
wa s use d in th es e m ea sur e m en ts. The fi rs t s eg me nt
wa s a n is othe r m al se gm en t f or 5 m in; th e s ec on d
se gm en t wa s a he a tin g se gm en t wit h a he a tin g r a te of
-1
10 K m in , a nd th e fi na l se gm en t wa s a n is ot he rm a l
se gm en t f or 5 m in. A m or e de ta il ed e xpe ri me nta l
8
pr oc e dur e is de sc r ibe d e lse whe r e. A sa pph ir e dis c
wa s use d a s th e st an dar d dur i ng he a t c ap ac ity me a -
sur e m en ts. The pr op er f unc ti onin g of th e c al or ime te r
wa s c he ck ed by th e m ea sur e m en t of th e m ola r he a t
Figure 2. Ar ra n g em en t us e d f or th e pr ep ar a ti on of
Ca H C l .
c ap ac it y of ThO . Two pe ll et s f or e ac h sa m ple w er e
2
st udie d, a nd a n a ve ra ge of a t le a st si x r ep r oduc ible
m ea sur e m en ts a t e ac h te m pe ra t ur e f r om e ac h s am ple
pe ll et is r ep or te d. Af te r th e m ea sur e m en ts, th e sa mpl es
we r e we igh ed a nd a na lyz e d by XR D to e nsur e pha s e
pu ri ty. The obs er ve d m as s lo sse s we r e le ss th an 0.02%
sho wing a n in sign ifi ca nt lo ss due to va por i za ti on.
C a( s ) þ H ðg Þ ! Ca H ðs Þ
2
2
Ca H2 ðs Þ þ C aC l 2 ðs Þ ! 2C aH Cl (s )
C a HB r wa s a ls o pr ep ar ed by ad op t in g a si mi la r
p ro c e d u re fo l lo wed f or Ca HCl pr ep ar at i on usi ng
p u ri fie d Ca B r . Ca Br was p rep ar ed by t he r eac ti on of
2
2
C a C O ([9 9 .9 5%, M / s. Al fa Aes ar , USA) wit h di s-
3
t i l l e d HB r (4 7 % so l ut i on , M / s. E. M er k, I nd ia ) . The 3. Results and Discussion
C a B r s o lu t io n wa s h eat ed ov er a ho t pl a te and dr ie d
2
3
.1 Molar heat capacities of ThO2
u n d e r fl o win g a rgo n ga s. I t was t he n p ur ifi e d by
h e a ti n g it a b o v e i ts me lt i ng po i nt i n a q uar t z c ru ci ble
p l a ce d in a q u a rtz v ess el i n a st r ea m of dr y arg on ga s
c o n ta in i n g HB r.
The m ola r he a t c ap ac it y of ThO wa s m ea sur e d in the
2
te m pe ra t ur es 333 –75 3 K a nd sho wn in F igu re 3 . The
r el a tiv e st an dar d de vi at ions of th e m ea sur e m ents a r e
wit hin 3%. The m ea sur e d m ola r he a t c ap ac it y va lue s
T h e c o mp o u n ds p rep ar ed wer e an al y ze d by XR D
M / s In e l, F ra n c e ) us i ng Cu K r adi a ti on . Th e XR D
(
a
of ThO a s a f unc ti on of te m pe ra t ur e we r e fi tte d to the
2
p a t t e rn s o f Ca HC l an d Ca HBr wer e ma tc he d wit h th e
J C PDS fi le s 0 4 - 08 -3 39 0 an d 04 - 08 -3 39 3, r es pe c-
7
t i v e ly . T h e s e s a m pl es wer e pe l le t iz ed , si n te r ed a nd
f oll owin g pol yno mi al e xpr e ssi on:
u s e d fo r h e a t c a p ac it y me asu r eme nt s . To ve r if y th e
p e rfo rm an c e o f DSC , t he mo la r he at ca pa ci t y o f ThO2
wa s a ls o d e te r min ed. Fo r t hi s, Th O po wd er ( 99.9 %
2
p u re , In d i an Ra r e Ea rt h s Lt d ., I nd ia ) was al so pe l-
l e ti z e d , s in t e re d at 15 0 0 °C f or 6 h an d u sed .
76
72
2
. 2 Differential scanning calorimetry
Th e mo l a r h e a t c ap ac it y of Ca HCl an d Ca HB r we r e
m e as u re d e mp l o y i ng a d if fe re nt i al sc an ni ng c al or i
m e t e r (M o d e l No . DSC 82 7e, M et t l er Tol e do,
Sw it z e rla n d ). T em pe ra t ure ca l ib ra t io n was ca rr ie d out
u s i ng h ig h p u re in di um an d zi n c ( 0.9 99 98 mas s f r ac -
t i o n p u ri ty , M /s . Imp ag AG, Swi t ze rl an d) me tal s.. The
s t a nd a rd u n c e rta in ty i n t he me asu r eme nt o f t em pe ra -
t u r e wa s d e te r min ed t o be ± 0 .4 K. Th e si n te re d pe ll ets
o f C aHCl an d CaHBr were seal ed in 40 ll Al- pa ns.
6
8
4
Present data
Fit line
Knacke et al.[6]
6
300
400
500
600
700
800
Temperature / K
Figure 3. Mol ar hea t C apaci t y of ThO 2 .

1
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J. Chem. Sci.
( 201 9) 13 1: 100
À
Á
70
65
60
55
50
À1
À1
À3
C \C aHC l [ J K m ol
p
¼
57:806 þ 16:420 Â 10 :T À 1:006
6
À2
 10 :T ð308À74 8 K Þ
ð2 Þ
-
1
-1
The st an dar d e rr o r of th e fi t is ± 0.2 7 J K mol .
The fi tte d c ur ve is a lso sho wn in F igu re 4 . The se da ta
on th e m ola r he a t c ap ac it y of C aHC l a re r ep or te d f or
th e fi rs t ti me . The m ea sur e d m ola r he a t c ap a c ity of
C aHC l is c om pa re d wit h th e da ta c om pute d by N eu-
Measured data
Fit
1 0
m an n–Kop p’ s r ule usi ng m ola r he a t c ap ac it y da ta of
9
C aH a nd C aC l in F igu re 4. The di sc ussi on on the
Neumann-Kopp's rule
2
2
ob ser ve d de vi at ions is gi ve n in S ec t. 3.4 . No da ta a r e
o
a va ila bl e in th e li te r at ur e f or th e S va lu e of C a HC l
98
a nd it wa s e sti ma te d f r om So
C aH 2, whi ch we r e 108 .370 J K m ol
-1
1 .999 J K m ol , r es pe ct ive ly . The C
300
400
500
600
700
800
2
Temperature / K
va lu es of C aCl a nd
2
29 8:15
-1
-1
Figure 4. Mo l ar he at ca pac ity of Ca HC l .
a nd
-1
9
4
p, 2 9 8 .1 5 K
À
Á
va lu e of C aHC l de te r mi ne d f r om th e fi t wa s 6.2%
lo wer th an th e va lu e e sti ma te d by in voki ng Ne uma nn–
Kop p’ s r ule a nd usi ng th e c or r esp ondi ng va lu es f r om
À1
À1
C \T h O [ J K mo l
p
2
À3
¼
7 3:6 7 1 þ 3:36 0 Â 1 0 :T À 1 :0 44
6
À2
9
-1
-1
 1 0 :T ð3 3 3À75 3 K Þ
ð1 Þ th e li te r at ur e f or C aC l ( 72.6 4 J K m ol ) a nd
o
2
2
-1
-1
C aH ( 37.0 0 J K m ol ) . Assu mi ng th at th e S
2 98:1 5
-1
-1
T h e s ta n d a rd e rr or o f t he fit i s ± 0 .29 J K m ol .
va lu e of C aHC l wil l a lso be 6.2 % lo wer th an the va lue
de r ive d f r om Ne um an n–Kop p’ s r ule , it wa s de d uc ed to
Th e fi tt ed p o ly n o mi al cu rv e i s sh own i n Fi g ur e 3. The
m o l a r h e a t c a p a c it y d at a of Th O f ro m t he com pi la -
2
-1
-1
m ol . Usi ng th is va lu e f or So
be 71 .3 J K
a nd
9
t i o n s o f Kn a c k e et al. ar e al s o sh own i n Fi g ur e 3 . The
p re s e n t d a ta a re i n g ood ag re em ent wi th t he da ta
29 8:1 5
e xpr e ssi on ( 2) f or th e m ola r he a t c ap ac it y, th e mol ar
e nth al py in cr e me nt s, e ntr op ie s a nd Gib bs e ne r gy
f unc ti ons of C aHC l we r e c om pute d a nd a re g ive n in
Ta ble 1 a lon g wit h th e m ea sur e d a nd fi tte d m ol ar he a t
c ap ac it y va lu es.
9
re p o rte d b y Kn a c k e et al. an d i t i s wi th i n ± 2 .0%.
3
. 2 Molar heat capacities of CaHCl
Th e me a s u re d mo la r h eat ca pa ci t y d at a of Ca HC l a re
s h o wn in F ig u re 4 an d gi v en i n Ta bl e 1. Th e r el a tiv e 3.3 Molar heat capacities of CaHBr
s t a nd a rd d e v ia ti o n s o f t he me asu r eme nt s ar e wit hin
3
fo l l o win g e x p re s si o n us i ng t he l ea st -s qu ar es m et hod:
%. T h e me a s u re d da t a o f Ca HCl wer e fit t ed to th e The m ea sur e d m ola r he a t c ap ac it y da ta of C aH B r is
sho wn in F igu re 5 . The obs er ve d r el a tiv e sta nda r d
Table 1. Th e rm od yn a m ic f un cti on s of Ca HC l.
-
C ( J K m ol
1
-1
À
Á
)
p
0
T
0
29 8 :1 5
H À H
À
Á
-
1
0
T
-1
S (J K m ol
-1
0
T
0
2 98 :1 5
-1
=T (J K mo l
-1
T ( K)
M ea s ur e d
F it
( J m ol
)
)
À G À H
)
2
3
3
3
4
4
5
5
5
6
6
7
7
9 8. 1 5
0 8
4 8
8 8
2 8
6 8
0 8
4 8
8 8
2 8
6 8
0 8
4 8
–
51 .4
52 .3
55 .2
57 .5
59 .3
60 .9
62 .2
63 .5
64 .6
65 .6
66 .5
67 .4
68 .3
0
71. 3
73. 0
79. 6
85. 7
91. 5
96. 8
101 .9
106 .7
111 .2
115 .4
119 .5
123 .4
127 .1
71. 3
71. 4
71. 9
73. 1
74. 5
76. 2
78. 0
79. 9
81. 9
83. 9
85. 9
87. 9
89. 9
5 2 .2
5 5 .0
5 7 .9
5 9 .5
6 0 .8
6 2 .2
6 3 .4
6 4 .4
6 5 .1
6 6 .6
6 7 .4
6 8 .8
511
26 6 3
49 1 9
72 5 7
96 6 2
12 12 6
14 64 0
17 20 1
19 80 3
22 44 5
25 12 4
27 83 9

J. Chem. Sci.
(2 01 9) 1 31 :1 00
P age 5 of 7
10 0
90
80
70
60
50
va lu e of C aHB r wil l a lso be 3.9 % lo wer th an th e va lue
de r ive d f r om Ne um an n–Kop p’s r ule , it wa s de duc e d
Measured data
Fit
-1
-1
f r om So
to be 82 .5 J K m ol
C aH 2 a nd C aB r , viz., 41 .999 J K m ol
1
va l ue s of
Neumann-Kopp's rule
29 8 :15
-
1
-1
a nd
2 9.704 J K m ol , r es pe ct ive ly . Usi ng th is va lue
f or So
a nd e xpr e ssi on ( 3) f or th e m ola r he a t
2
-1
-1
9
29 8:15
c ap ac it y, th e m ola r e nth al py in cr e me nt s, e ntr opie s a nd
Gib bs e ne rg y f unc ti ons of C aHB r we r e c om pu te d a nd
a re gi ve n in Ta ble 2 a lon g wit h th e m ea sur e d a nd
fi tte d m ola r he a t c ap ac it y va lu es.
3.4 Deviations of Cp from Neumann–Kopp’s rule
300
400
500
600
700
800
Temperature / K
Ne um an n–Kop p’s r ule ( NKR) is a n a ddi tiv e r ule
whe r ei n a n e sti ma te of m ola r he a t c ap ac it ie s of a
c om poun d is a rr i ve d by th e st oic hi ome tr i c a dditi on of
m ola r he a t c ap ac it ie s of th e in divi dua l c ompo ne nt
Figure 5. Mo la r he at ca pac it y of Ca HB r .
1
0
c om poun ds, m ostl y a ppl ie d to oxi de s. Le it ne r et al.
d e v ia ti o n s o f th e me asu r eme nt s ar e i n t he r an ge of
– 3 %. T h e me a s u r ed da t a wer e fit t ed t o t he f oll owin g
e x p re s s io n u s in g t he l ea st -s qu ar es me th od :
ha ve de sc r ibe d th e po ssib le c au se f or th e de vi atio ns of
m ea sur e d he a t c ap ac it y a nd th at obt a ine d by N KR f or
m ixe d oxi de s. I n th is st udy, it is a tte m pte d f or C a HC l
a nd C aHB r . A goo d e sti ma te is ob ta ine d whe ne ve r the
c ry sta l st ru ct ur es of th e pr od uct s a nd r ea c ta nt s a r e the
sa m e or wit h m ini mum di stor t ions . F ur the r , the de vi-
a tio n c an be du e to th e di ff e r en ce in th e m ola r volu me s
of th e pr od uct s a nd th e r ea c ta nt s. As se e n f r om
F igu re 4, th e m ea sur e d m ola r he a t c ap ac it ie s of C a HC l
we r e lo wer th an th e NKR va lu es be lo w *370 K a nd
hi ghe r a bove th is te m pe ra t ur e. I n th e c as e of C a HB r
( Fi gur e 5) , th e m ea sur e d m ola r he a t c ap ac i tie s of
C aHB r we r e hi ghe r th an th e NKR va lu es f or the e ntir e
te m pe ra t ur e r an ge . The c ry sta l st ru ct ur es of C a H2
1
À
Á
À1
À1
À3
C \Ca HB r [ J K mo l
p
¼
5 6:5 3 4 þ 4 4:8 80 Â 1 0 :T À 1 :4 81
6
À2
 1 0 :T ð3 2 3À71 3 K Þ
ð3 Þ
-1
-1
T h e s ta n d a rd e rr or o f t he fit i s ± 0 .26 J K m ol .
Th e le a s t s q u a res fit t ed cu rv e i s al s o sh own in
Fi g u re 5. T h e re is no he at ca pa ci t y da t a r epo r te d in th e
l i t er a tu re fo r Ca HB r, an d t he p res en t da t a ar e r ep or te d
o
fo r th e fi rs t ti me . S 29 8 va l ue of Ca HBr was est im a te d
a s in th e c a s e o f Ca HCl . Th e ex pe ri me nt a l Cp, 2 98 . 1 5 K
v a l ue o f Ca HB r d et er mi ned f ro m t he fit was 3.9 %
l o w e r th a n th e v al u e es t im at ed by Neu ma nn –Kop p’ s
ru l e u s in g th e co rr es po nd i ng va l ue s f ro m th e
(
(
or tho rh om bic ) ,
or tho rh om bic ) C aHB r ( Te tr a gona l) a nd C aHC l ( Te -
C aB r 2
( te tr a gona l )
C a Cl2
9
-1
-1
fo r Ca H 2 ( 37 .00 J K mo l ) a nd
l i t era tu r e
C a B r (7 3 . 9 2 J K mo l ) . Ass um in g t ha t t he S
tr a gon al ) a re not th e sa m e. He nc e, th e bon din g e nvi-
r onm e nt, bon din g ty pe a nd c oor di na tion num b e rs a r e
-
1
-1
o
29 8:15
2
Table 2. Th e rm od yn a m ic f un cti on s of Ca HB r.
-
C ( J K m ol
1
-1
À
Á
À
Á
)
p
0
T
0
2 98:1 5
0
T
0
2 98 :15
H À H
À G À H
=T
)
-
1
0
T
-1
S (J K m ol
-1
-1
(J K m o l
-1
T ( K)
M e as ur e d
F it
(J m ol
)
)
2
3
3
3
4
4
5
5
5
6
6
7
9 8 .1 5
2 3
5 3
9 3
3 3
7 3
1 3
5 3
9 3
–
53 .3
56 .8
60 .5
64 .6
68 .1
71 .1
73 .9
76 .5
78 .9
81 .2
83 .5
85 .6
0
82. 5
86. 9
92. 1
98. 8
105 .3
111 .4
117 .3
123 .0
128 .4
133 .6
138 .7
143 .5
82. 5
82. 7
83. 3
84. 5
86. 1
88. 0
90. 1
92. 2
94. 5
96. 8
99. 1
101 . 5
57 .0
60 .7
64 .5
67 .8
70 .9
74 .1
76 .7
79 .2
81 .5
83 .0
85 .9
136 9
313 1
563 4
828 9
110 74
139 77
169 86
200 95
232 99
265 94
299 76
3 3
7 3
1 3

1
0 0 Pa g e 6 o f 7
J. Chem. Sci.
( 201 9) 13 1: 100
Table 3. C o mp a ri s on of un it ce ll vo lu m es of te rna ry com pou nds (V TC ) and cal cul at ed uni t cel l vol um e s us i ng u ni t c el l
v o lu me s o f b i n ar y co m po un ds ( V BC ) .
3
Un it cel l vo l um e/ for m u l a uni t (A )
˚
Ce ll vo lu m e
N o. of fo rm ul a uni t
(Z)
Vol u m e
cha ng e
3
˚
Co mp o u n d s
St ru ct ur e
( A )
VTC
V B C
Ca HC l
Ca H B r
Ca H 2
Ca C l 2
Ca B r 2
Te t ra go na l
Te t ra go na l
Or th o r ho m bi c
Or th o r ho m bi c
Te t ra g on a l
10 1. 75
11 7. 75
14 3. 77
16 7. 73
20 3. 32
2
2
4
2
2
5 0. 88 ‘ (C aH ? C a C l ), 59. 91
17. 75 %
16. 85 %
2
2
5 8. 88 ‘ (C aH ? C a B r ), 68. 80
2
2
3 5. 94
8 3. 87
10 1. 66
–
–
–
–
–
–
* Un it c el l v o l u me s w er e ta ken f ro m J CP D S fi le s 04- 08- 339 0, 04- 08- 3393 , 00- 31- 026 6, 00- 24- 0 223 and 01-7 1 - 5 40 6
r es pe ct i v el y fo r C aH Cl , Ca HB r, Ca H , C a C l an d C aB r
2
2
2
.
a l so n o t th e s a me i n t he pr o du ct an d t he st ar t ing Thu s th e de vi at ions f r om th e NKR a re a ttr i bute d to the
c o mp o u n d s. Al l th e se co ul d be t he co nt r ib ut i ng f ac t or s di lut ion te r m C . in th e m ea sur e m en t r an ge of i nte r e st.
fo r th e d if fe re n c e i n t he me asu r ed an d es t im at ed m ola r The di ff e r en ce in m ola r vo lum es of c om poun ds , the ir
d i l
h e a t c a p a c ity v a lu e s.
M o la r h e a t c ap ac it y ( C ) ca n be r ega rd e d a s a pr e ssi bili ty f ac t or s a s gi ve n by th e f oll owin g e xpr e s-
te m pe ra t ur e c oe ffi c ie nt s of e xpa nsi ons, a nd c om-
p
c o n tr ib u ti o n d u e t o t he l at t ic e v ib ra ti o ns ( C p h ) si on wil l a ff e c t th e C d i l va lu es.
(
(
p h o n o n s ), la t ti ce di l at i on s ( C ) an d ot h er f ac t or s
di l
À
Á
À
Á
2
2
A
DC =T ¼ V a =b
À x V a =b
dil
AB AB
AB
A
A
A
Cot h er s ) s u c h a s d u e t o el e ct ro ns i nv ol ve d i n con duc -
À
Á
2
B
À x V a =b
ð7 Þ
t i o n , e x c it a tio n of l oc al i zed el e ct ro ns an d va c an cy
fo r m a tio n , e tc . T hi s ca n be ex pr es se d as ,
B
B
B
whe r e AB r ep r ese nt s th e te r na r y c om poun d f or me d
ð4 Þ f r om th e c onst itu en t bi na ry c om poun ds A a nd B .
C ¼ C þ C þ C
F o r p u re io n i c cr ys t al s l ik e Ca HCl an d Ca HB r , th e
c o n tr ib u ti o n s d u e t o ex ci t at i on s of l oc al i zed and c on-
d u c ti o n e le c tr o n s ar e ex pe ct ed t o b e l es s. Bu t c ont ri -
p
ph
dil
o the rs
The c ry sta l st ru ct ur e a nd uni t c el l vol um e pe r f or -
m ula un it f or bot h bi na ry c om poun ds a nd te r na r y
c om poun ds a re gi ve n in Ta ble 3 . The vo lum e c ha nge
due to th e f or ma t ion of te r na r y c om poun d f o rm the
c or r esp ondi ng bi na ry c om poun ds is a lso li ste d . I t c a n
be se e n th at th e te r na r y c om poun d f or ma t io n w as
a cc om pa ni ed by a r ed uc tio n in th e c el l v olume .
Howe ve r , to c al cu la te c ont ri but ing te r ms , it is ne c e s-
sa r y to ha ve da ta on a a nd b pa r am e te r s whi ch a r e not
a va ila bl e in th e li te r at ur e.
000
b u t i o n s fro m v a c a nc ie s o f ca l ci um V an d h ydr og en
ꢀ
Ca
V co u l d n o t b e ru le d ou t . Har mo ni c an d an ha r mo nic
v i b ra ti o n s c o n tr ib ut e t o t he p hon o n v ib ra ti o ns . C , i s
g i v en b y th e fo l lo win g ex pr es si o n:
H
d i l
2
C di l ¼ C À C ¼ TVa =b ð5 Þ
wh e re in th e C is t he mo la r he at ca pa ci t y at con sta nt
p
v
v
v o l um e , V is th e mo la r vo l ume , a i s t he is oba r ic
v o l um e e x p a n s io n, b i s t he i so th er ma l co mp re ssi bil it y.
At lo w te m p e ra tu re s, ha rm on ic ph o non v ib ra ti ons a re
d o mi n a tin g b u t, a t h ig h t emp er at u re s, t he di la ta tio n
a n d a n -h a rm o n ic co rr ec t io n t er ms d omi na t e. The ha r -
m o ni c p a rt b e c o me s eq ua l t o Du lo ng –P et i t l aw li mi t-
i n g v a lu e o f 3 NR, wh er e N i s t he nu mb er o f at om s pe r
fo r m u la u n it a n d R i s t he un i ve rs al g as co ns t ant .
4
. Conclusions
The m ola r he a t c ap ac it y m ea sur e m en ts we r e c a r ri e d
out f or C aHC l a nd C aHB r usi ng DS C a nd th e c or r e -
spo ndi ng e sti ma te d th er m odyn am i c f unc ti ons of the
two c om poun ds we r e de te r mi ne d. The hi gh- te mpe r a -
tu re m ola r he a t c ap ac it y da ta of C aHC l a nd C aH B r a r e
r ep or te d f or th e fi rs t ti me .
C ¼ C þ C þ C
p
ha r
anh
d il
2
¼
3 NR þ C þ TV a =b
ð6 Þ
a
n
h
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a
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e
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o
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