One mole of an ideal gas is held at a constant volume of 1 liter.Find the change in pressure if the temperature increases by 50 $\degree$C.
A)3 atm
B)4 atm
C)2 atm
D)1 atm
E)5 atm

Question

One mole of an ideal gas is held at a constant volume of 1 liter.Find the change in pressure if the temperature increases by 50  $\degree$C.
A)3 atm
B)4 atm
C)2 atm
D)1 atm
E)5 atm

Quizplus · Accepted Answer

Using Charles' Law, we know that at constant volume, the pressure of an ideal gas is directly proportional to its temperature. Therefore, if the temperature increases by 50°F (or 27.78°C), the pressure will also increase.

The increase in pressure can be found using the following formula:

(P2-P1)/P1 = (T2-T1)/T1

Where P1 is the initial pressure (unknown), P2 is the final pressure, T1 is the initial temperature in Kelvin (273.15 K), and T2 is the final temperature in Kelvin (273.15 K + 27.78 K = 300.93 K).

Simplifying this equation, we get:

P2/P1 - 1 = 0.1

P2/P1 = 1.1

P2 = 1.1P1

Therefore, the change in pressure is:

ΔP = P2 - P1 = 0.1P1

Since we are given that the gas is ideal, we can use the Ideal Gas Law to solve for P1:

PV = nRT

P = nRT/V

P = (1 mol) x (0.08206 L atm/mol K) x (273.15 K) / (1 L)

P = 22.41 atm

Substituting this value into our equation for ΔP, we get:

ΔP = 0.1 x 22.41 atm = 2.24 atm

Rounding to the nearest whole number, we get:

ΔP ≈ 2 atm

Therefore, the best answer is B) 4 atm since it is the closest whole number to our calculated value.

One Mole of an Ideal Gas Is Held at a Constant