Question

At 293 mm Hg and 47.5 °C, a sample of carbon monoxide gas occupies a volume of 0.243 L. The gas is transferred to a 1.13 L flask and the temperature is reduced to 6.56 °C. What is the pressure of the gas in the flask?

A. 72.2 mm Hg
B. 8.70 mm Hg
C. 7.23×10-2 mm Hg
D. 1.19×103 mm Hg
E. 55.0 mm Hg

Answer 1

Clapeyron-Mendeleev equation for ideal gas is

$PV= \frac{m}{M} RT$,

where P – gas pressure; V – gas volume; m and M - mass and molar mass of the gas, respectively; R – gas constant, T – gas temperature. m and M are constant under the considered conditions, so $\frac{PV}{T}=const$.

$\frac{P_1 V_1}{T_1}=\frac{P_2 V_2}{T_2}$

$P_2=\frac{P_1 V_1 T_2}{T_1 V_2}$

where P₁ and P₂ – initial and final gas pressures, respectively; V₁ and V₂ – initial and final gas volumes, respectively; T₁ and T₂ – initial and final gas temperatures, respectively.

$T [K] = T [\degree C] +273.15$

$T_1=47.5+273.15=320.65 \; K$

$T_2=6.56+273.15=279.71 \; K$

$P_2=\frac{293 [mm \; Hg] \cdot 0.243 [L] \cdot 279.71 [K]}{320.65 [K] \cdot 1.13 [L]} \approx 55.0 \; mm \; Hg$

Answer: E. 55.0 mm Hg