Numerical problem from ideal gas equation

Given:

• Initial volume, \( V_1 = 1638 \) cc
• Initial pressure, \( P_1 = 76, \) cm Hg (Standard Pressure)
• Initial temperature, \( T_1 = 0^\circ C = 273\) K
• Final pressure, \( P_2 = 57 \) cm Hg
• Final temperature, \( T_2 = -20^\circ C = 253 \) K
• Final volume, \( V_2 = ? \)

Using the Combined Gas Law:

\( \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2} \)

Rearranging to find \( V_2 \):

\( V_2 = \frac{P_1 \times V_1 \times T_2}{P_2 \times T_1} \)

Substitute the values:

\( V_2 = \frac{76 \times 1638 \times 253}{57 \times 273} \)

\( V_2 = \frac{31,587,336}{15,561} \approx 2030.5, \) cc

Final Answer: The volume of the gas at 57 cm Hg pressure and –20°C temperature is approximately 2030.5 cc.