College

If a cylinder contains 38.6 g of [tex]CO_2[/tex] in 18.0 L at 475 K, what is the pressure (in atm)? Be sure your answer has the correct number of significant figures.

[tex]\square[/tex] atm

Answer :

To determine the pressure of [tex]\(CO_2\)[/tex] in a cylinder, we can use the ideal gas law equation:

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

where [tex]\( P \)[/tex] is the pressure, [tex]\( V \)[/tex] is the volume, [tex]\( n \)[/tex] is the number of moles, [tex]\( R \)[/tex] is the ideal gas constant, and [tex]\( T \)[/tex] is the temperature in Kelvin.

Let's solve this step-by-step:

1. Given Values:
- Mass of [tex]\( CO_2 \)[/tex] = 38.6 g
- Volume ([tex]\( V \)[/tex]) = 18.0 L
- Temperature ([tex]\( T \)[/tex]) = 475 K
- Molar Mass of [tex]\( CO_2 \)[/tex] = 44.01 g/mol
- Ideal Gas Constant ([tex]\( R \)[/tex]) = 0.0821 L·atm/(mol·K)

2. Calculate the number of moles ([tex]\( n \)[/tex]) of [tex]\( CO_2 \)[/tex]:
[tex]\[
n = \frac{\text{mass of } CO_2}{\text{molar mass of } CO_2} = \frac{38.6 \, \text{g}}{44.01 \, \text{g/mol}} \approx 0.877 \, \text{mol}
\][/tex]

3. Use the Ideal Gas Law to find the pressure ([tex]\( P \)[/tex]):
[tex]\[
P = \frac{nRT}{V} = \frac{(0.877 \, \text{mol})(0.0821 \, \text{L·atm/mol·K})(475 \, \text{K})}{18.0 \, \text{L}}
\][/tex]

4. Calculate the Pressure:
[tex]\[
P \approx 1.90 \, \text{atm}
\][/tex]

Therefore, the pressure of [tex]\( CO_2 \)[/tex] in the cylinder is approximately 1.90 atm. Use this value to fill in the answer:

[tex]\[ \text{Pressure} = 1.90 \, \text{atm} \][/tex]

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