Question

learn by doing
a sample of nitrogen, n₂, occupies 45.0 ml at 352 k and 625 torr. the sample of gas is cooled and the new pressure is measured to be 455 torr. what is the cooled temperature of the gas? first, identify the following variables from the problem. enter the numeric value on the right and use the drop down menu to choose the correct unit for the variable. for the unknown variable enter a question mark on the left.
p₁ =
t₁ =
p₂ =
t₂ =
calculate the value of the unknown variable. include the calculated value on the left and use the drop - down menu to choose the correct unit.

Explanation:

Step1: Identify variables

• \(P_1 = 625\) torr (initial pressure)
• \(T_1 = 352\) K (initial temperature)
• \(P_2 = 455\) torr (final pressure)
• \(T_2\) is the unknown (final temperature)

Step2: Use Gay - Lussac's Law (\(\frac{P_1}{T_1}=\frac{P_2}{T_2}\))

$$T_2=\frac{P_2\times T_1}{P_1}$$

$$T_2=\frac{455\space torr\times352\space K}{625\space torr}$$

$$T_2 = 257\space K$$

Answer:

• \(P_1 = 625\), unit: torr
• \(T_1 = 352\), unit: K
• \(P_2 = 455\), unit: torr
• \(T_2 = 257\), unit: K