Questions: 19. A gas at 300 K had its pressure changed from of 0.8 atm to 0.5 atm . If the volume is held constant, what will be the new temperature of the gas?

Solution Steps

For a gas at constant volume, the relationship between pressure and temperature is given by Gay-Lussac's Law, which states:

\[ \frac{P_1}{T_1} = \frac{P_2}{T_2} \]

where:

• \(P_1\) and \(T_1\) are the initial pressure and temperature,
• \(P_2\) and \(T_2\) are the final pressure and temperature.

From the problem, we know:

• Initial pressure, \(P_1 = 0.8 \, \text{atm}\)
• Final pressure, \(P_2 = 0.5 \, \text{atm}\)
• Initial temperature, \(T_1 = 300 \, \text{K}\)

Rearrange the equation to solve for \(T_2\):

\[ T_2 = \frac{P_2 \cdot T_1}{P_1} \]

Substitute the known values:

\[ T_2 = \frac{0.5 \, \text{atm} \cdot 300 \, \text{K}}{0.8 \, \text{atm}} \]

Calculate \(T_2\):

\[ T_2 = \frac{150}{0.8} = 187.5 \, \text{K} \]

Final Answer