Question

A container of carbon dioxide (CO2) has an initial temperature of 170 K with a pressure of 50 kPa. When the container is heated the pressure is measured at 283 kPa. The volume is constant at 12 L throughout. What is the final temperature of the carbon dioxide (CO2)?
A. 391.0 K
B. 1179.16 K
C. 6.94 K
D. 962.2 K

Answer 1

Answer:

$\boxed{\text{D. 962 K}}$

Explanation:

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

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

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

Data:

p₁ =    50 KPa; T₁ = 170 K

p₂ = 283 KPa; T₂ = ?

Calculations:

$\begin{array}{rcl}\dfrac{50}{170} & = & \dfrac{283}{T_{2}}\\\\0.294 & = & \dfrac{283}{T_{2}}\\\\0.294T_{2} & = & 283\\\\T_{2} & = &\dfrac{283}{0.294}\\\\ & = &\textbf{962 K}\\\end{array}\\\text{The final temperature of the carbon dioxide is }\boxed{\textbf{962 K}}$