College

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

Note: Reference the Fundamental Constants table for additional information.

Answer :

Sure, let's solve the problem step-by-step using the ideal gas law equation, which is [tex]\( PV = nRT \)[/tex].

1. Identify the given values:
- Mass of carbon monoxide (CO): 38.6 g
- Volume of the cylinder: 18.0 L
- Temperature: 475 K
- Molar mass of CO (carbon monoxide): approximately 28.01 g/mol
- Ideal gas constant [tex]\( R \)[/tex]: 0.0821 L atm / (mol K)

2. Convert the mass of CO to moles:
To find the number of moles ([tex]\( n \)[/tex]), use the formula:
[tex]\[
n = \frac{\text{mass}}{\text{molar mass}}
\][/tex]
[tex]\[
n = \frac{38.6 \, \text{g}}{28.01 \, \text{g/mol}} \approx 1.3781 \, \text{mol}
\][/tex]

3. Use the ideal gas law to find the pressure:
The ideal gas law equation is [tex]\( PV = nRT \)[/tex]. We need to solve for the pressure [tex]\( P \)[/tex]:
[tex]\[
P = \frac{nRT}{V}
\][/tex]
Substituting the known values:
[tex]\[
P = \frac{(1.3781 \, \text{mol}) \times (0.0821 \, \text{L atm / (mol K)}) \times (475 \, \text{K})}{18.0 \, \text{L}}
\][/tex]
[tex]\[
P \approx 2.986 \, \text{atm}
\][/tex]

4. Significant Figures:
The given data specifies the cylinder contains 38.6 g of CO, which has three significant figures. Therefore, our final answer should also be expressed with three significant figures.

Thus, the pressure in the cylinder is approximately [tex]\( 2.986 \, \text{atm} \)[/tex].

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