Answered

"What is the pressure of 5.0 mol nitrogen (N2) gas in a 2.0 L container at 268
K?
The universal gas constant is 0.0821 L-atm/mol-K.)
A. 8.8 atm
о
B. 220 atm
0
C. 0.018 atm
D. 55 atm



Answer :

GinnyAnswer
To determine the pressure of 5.0 moles of nitrogen gas in a 2.0-liter container at a temperature of 268 K, given the universal gas constant 0.0821 L-atm/(mol·K), we use the Ideal Gas Law:

[tex]\[ PV = nRT \][/tex]

Where:
- [tex]\( P \)[/tex] is the pressure in atmospheres (atm)
- [tex]\( V \)[/tex] is the volume in liters (L)
- [tex]\( n \)[/tex] is the number of moles (mol)
- [tex]\( R \)[/tex] is the universal gas constant, 0.0821 L-atm/(mol·K)
- [tex]\( T \)[/tex] is the temperature in Kelvin (K)

Rearrange the equation to solve for pressure [tex]\( P \)[/tex]:

[tex]\[ P = \frac{nRT}{V} \][/tex]

Substitute the given values into the equation:

[tex]\[ P = \frac{(5.0 \, \text{mol}) \times (0.0821 \, \text{L-atm/mol-K}) \times (268 \, \text{K})}{2.0 \, \text{L}} \][/tex]

Now, perform the multiplication and division:

[tex]\[ P = \frac{5.0 \times 0.0821 \times 268}{2.0} \][/tex]
[tex]\[ P = \frac{110.014}{2.0} \][/tex]
[tex]\[ P = 55.007 \, \text{atm} \][/tex]

Therefore, the pressure of the nitrogen gas in the container is [tex]\( 55.007 \, \text{atm} \)[/tex]. When rounded to two significant figures, the result is:

[tex]\[ P \approx 55 \, \text{atm} \][/tex]

Thus, the correct answer is:
D. 55 atm

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