Quartz phase transition I) A quartz crystal has a volume of 7.5 ml at 298 K and
ID: 802205 • Letter: Q
Question
Quartz phase transition I) A quartz crystal has a volume of 7.5 ml at 298 K and 0.1 MPa. What is the volume of the crystal at 840K and 12.3 MPa if: a) ?= 1.4654 × 10-5 (K-1) and ?T= 2.276 × 10-11 (Pa-1) and ? and ?T are independent of T and P; b) ? = 1.4310 × 10-5 (K-1) + 1.1587 × 10-9 (K-2) × T and ?T = 1.8553 × 10-11(Pa-1) + 7.9453 × 10-8/P. II) calculate the total enthalpy upon heating of 100 g of quartz from 25° C to 900° C. Quartz undergoes a phase transition from ?-quartz to ?-quartz at 575° C. The enthalpy of this phase transition is ?Htr =0.411 kJ/mol. Use the Maier-Kelly heat capacity data in the table.
Explanation / Answer
dT=T2-T1=840-298=542 K
dP=P2-P1=12.3-0.1=12.2atm
delta V=V2-V1
V2=??
V1=7.5mL
delta S=41.34-41.84=0.5
delta Cp=0.03431-0.00812=0.002619
dT/dP=delta alpha*V*T/delta Cp
542/12.2=1.4654*10^-5*(V2-7.5)*(542)/0.002619
44.42=794.2*10^-5(V2-7.5)*/0.002619
44.42*0.002619/794.2*10^-5=V2-7.5
0.116/794.2*10-5=V2-7.5
1.4*10=V2-7.5
14+7.5=V2
21.5=V2
b.dT/dP= delta alpha*V*T/delta Cp
dT=542 K
dP=12.2
delta alpha=1.4310*10-5(K-1)+1.1587*10^-9(K-2)*(K)*
delta CP=0.002619J/K-mol
542/12,2=1.4310*10-5(K-1)+1.1587*10^-9* 542/0.002619
44.42=1.4310*10-5+1.1587*10-9*542(V2-7.50)*542/0.002619
44.42*0.002619=1.4310*10-5+1.1587*10-9*542(V2-7.5)*542
0.116/542*542(1.4310*10-5+1.1587*10-9)=V2-7.5
0.116/293764=10-5(1.4310+1.1587*10-4)
3.9*10-7=10-5(1.4310+0.0001587)
3.9*10-7=10-5*1.43
3.9*10-7/1.43*10-5
2.7*10-2=V2-7.52
2.7*10-2+7.52
=0.027+7.52=V2
7.547=V2