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

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

Step-by-step 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.

`(p_(1))/(T_(1)) = (p_(2))/(T_(2))`

Data:

p₁ = 50 KPa; T₁ = 170 K

p₂ = 283 KPa; T₂ = ?

Calculations:

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