Question

Determine the new temperature of a sample of gas if the pressure changes from 0.500 atm to 0.750 atm, and the gas had an initial temperature of 315 K. The volume and number of gas particles is held constant.
210. K

118 K

2.12 x 10-3 K

473 K

Answer 1

Answer:

$\boxed{\text{472 K}}$

Explanation:

The volume and number of moles are constant, so we can use Gay-Lussac’s Law:

At constant volume and number of particles, the pressure exerted by a gas is directly proportional to its temperature.

$\dfrac{p_{1}}{T_{1}} = \dfrac{p_{2}}{T_{2}}$

Data:

p₁ = 0.500 atm; T₁ = 315 K

p₂ = 0.750 atm; T₂ = ?

Calculations:

$\begin{array}{rcl}\dfrac{0.500}{0.750} & = & \dfrac{315}{T_{2}}\\\\0.6667 & = & \dfrac{315}{T_{2}}\\\\0.6667T_{2} & = & 315\\\\T_{2} & = &\dfrac{315}{0.6667}\\\\ & = &\textbf{472 K}\\\end{array}\\\text{The new temperature of the gas is }\boxed{\textbf{472 K}}$