A container of gas with a volume of 952 mL at a temperature of 321 K exerted a pressure of 108 atm. Calculate the pressure of this same amount of gas in a 1.236 L container at a temperature of 59 oF.

Question

A container of gas with a volume of 952 mL at a temperature of 321 K exerted a pressure of 108 atm. Calculate the pressure of this same amount of gas in a 1.236 L container at a temperature of 59 oF.

87.3 atm

7.46 X 10 to the power of 4 atm

3.96 X 10 squaredatm

38.1 atm

Answer 1

To solve this problem, we can use the ideal gas law equation:

PV = nRT

Where:
P = pressure
V = volume
n = amount of gas (in moles)
R = ideal gas constant
T = temperature (in Kelvin)

First, let's find the amount of gas:

To find the amount of gas, we can use the formula:

n = PV / RT

Given:
P1 = 108 atm
V1 = 952 mL = 0.952 L
T1 = 321 K

Rearranging the formula to solve for n, we have:

n = (P1 * V1) / (R * T1)

Next, let's find the pressure of the gas in the new container:

Given:
V2 = 1.236 L
T2 = 59 °F = (59 - 32) °C = (5/9)(59 - 32) K

Now, we can find the pressure using the equation:

P2 = (n * R * T2) / V2

Now, let's substitute the values into the equations and calculate the pressure:

First, we need to convert the mL unit to L for V1:

V1 = 952 mL = 0.952 L

We also need to convert the temperature from Fahrenheit to Kelvin for T2:

T2 = (5/9)(59 - 32) + 273.15 = 288.705 K

Now, let's substitute the values and calculate n:

n = (108 atm * 0.952 L) / (0.0821 atm·L/mol·K * 321 K) ≈ 3.76 mol

Now, let's substitute the values and calculate P2:

P2 = (3.76 mol * 0.0821 atm·L/mol·K * 288.705 K) / 1.236 L ≈ 87.3 atm

Therefore, the pressure of the gas in the 1.236 L container at 59 °F is approximately 87.3 atm.

So, the correct answer is 87.3 atm.