Question

question 7 of 30
what is the pressure of 0.5 mol nitrogen (n₂) gas in a 5.0 l container at 203 k?
(the universal gas constant is 0.0821 l·atm/mol·k.)

a. 170 atm
b. 42 atm
c. 1.7 atm
d. 0.60 atm

Explanation:

Step1: Recall Ideal Gas Law

The ideal gas law is \( PV = nRT \), where \( P \) is pressure, \( V \) is volume, \( n \) is moles, \( R \) is gas constant, and \( T \) is temperature. We need to solve for \( P \), so rearrange the formula to \( P=\frac{nRT}{V} \).

Step2: Identify Given Values

We have \( n = 0.5\space mol \), \( R = 0.0821\space L\cdot atm/mol\cdot K \), \( T = 203\space K \), and \( V = 5.0\space L \).

Step3: Substitute Values into Formula

Substitute the values into \( P=\frac{nRT}{V} \):
\( P=\frac{0.5\space mol\times0.0821\space L\cdot atm/mol\cdot K\times203\space K}{5.0\space L} \)

Step4: Calculate Numerator First

Calculate the numerator: \( 0.5\times0.0821\times203 = 0.5\times16.6663 = 8.33315 \)

Step5: Divide by Volume

Now divide by \( V = 5.0\space L \): \( P=\frac{8.33315}{5.0}\approx1.7\space atm \)

Answer:

C. 1.7 atm