Question

how many moles of oxygen must be placed in a 3.00 l container to exert a pressure of 2.00 atm at 25.0 °c?

formula: \\(pv = nrt\\) (\\(r = 0.0821 \frac{\text{l}\cdot\text{atm}}{\text{mol}\cdot\text{k}}\\))

which variables are given? choose three correct answers.

• pressure
• moles
• volume
• temperature

which variables are unknown?

• volume
• temperature
• pressure
• moles

select the correct algebraic form for the equation to be used for this calculation.

• \\(n = \frac{rv}{pt}\\)
• \\(n = \frac{pv}{rt}\\)
• \\(n = \frac{rt}{pv}\\)

solve the problem for the moles of oxygen:
\\(\text{mol } \text{o}_2\\)

Explanation:

Identify given variables

Using the Pressure-Volume-Temperature Relationships knowledge point:

• Volume \(V = 3.00\text{ L}\)
• Pressure \(P = 2.00\text{ atm}\)
• Temperature \(T = 25.0^\circ\text{C} = 298.15\text{ K}\)

Thus, the given variables are pressure, volume, and temperature.

Identify unknown variables

Using the Gas Laws knowledge point:

• The question asks "How many moles of oxygen...".
• Therefore, the unknown variable is moles (\(n\)).

Rearrange the ideal gas law

Using the Gas Laws knowledge point:

• Start with the ideal gas law:

$$PV = nRT$$

• Isolate \(n\) by dividing both sides by \(RT\):

$$n = \frac{PV}{RT}$$

Calculate the moles of oxygen

Using the Gas Laws knowledge point:

• Substitute the values into the rearranged equation:

$$n = \frac{(2.00\text{ atm})(3.00\text{ L})}{(0.0821\text{ L}\cdot\text{atm}/(\text{mol}\cdot\text{K}))(298.15\text{ K})}$$

• Compute the value:

$$n \approx \frac{6.00}{24.478} \approx 0.245\text{ mol}$$

Answer:

Question 1: Which variables are given? Choose three correct answers.

• pressure
• volume
• temperature

Question 2: Which variables are unknown?

• moles

Question 3: Select the correct algebraic form for the equation to be used for this calculation.

$$n = \frac{PV}{RT}$$

Question 4: Solve the problem for the moles of oxygen.

\(0.245\text{ mol O}_2\)