Question

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 = 625 torr t₁ = 352 k p₂ = 455 torr t₂ = 257 k correct. this is the initial pressure before any conditions are changed. correct. torr is the given unit of pressure in this problem. correct. this is the initial temperature before any conditions are changed. correct. kelvin (k) is the given unit of temperature in this problem. correct. this is the pressure after the condition of temperature is changed. correct. torr is the given unit of pressure in this problem. incorrect. review the hint and try again. correct. kelvin (k) is the given unit of temperature in this problem. 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: Apply Gay - Lussac's Law

Gay - Lussac's Law is \( \frac{P_1}{T_1}=\frac{P_2}{T_2}\), where \(P_1\) is the initial pressure, \(T_1\) is the initial temperature, \(P_2\) is the final pressure, and \(T_2\) is the final temperature.
We need to solve for \(T_2\). Rearranging the formula gives \(T_2=\frac{P_2T_1}{P_1}\).

Step2: Substitute the given values

We are given \(P_1 = 625\) torr, \(T_1=352\) K, and \(P_2 = 455\) torr.
Substitute these values into the formula: \(T_2=\frac{455\times352}{625}\).
First, calculate \(455\times352 = 455\times(300 + 50+2)=455\times300+455\times50 + 455\times2=136500+22750+910 = 159160\).
Then, \(T_2=\frac{159160}{625}=254.656\approx255\) K.

Answer:

255 K