Multiple Choice
A sample of O_2 gas occupies 75 L at 2.0 atm and 300 K. What is the number of moles of O_2 present in the sample? (Use R = 0.0821 L·atm·mol^{-1}·K^{-1})
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7. Gases
The Ideal Gas Law
Multiple Choice
What is the amount of gas, in moles, that occupies 60.82 L at 31.0 °C and 367 mm Hg according to the ideal gas law?
A
2.45 mol
B
0.98 mol
C
3.60 mol
D
1.20 mol
Verified step by step guidance1
Identify the known variables from the problem: volume \(V = 60.82\ \text{L}\), temperature \(T = 31.0\ ^\circ\text{C}\), and pressure \(P = 367\ \text{mm Hg}\).
Convert the temperature from Celsius to Kelvin using the formula \(T(K) = T(^\circ C) + 273.15\), so \(T = 31.0 + 273.15\) K.
Convert the pressure from mm Hg to atm because the ideal gas constant \(R\) is commonly given in atm. Use the conversion \(1\ \text{atm} = 760\ \text{mm Hg}\), so \(P(\text{atm}) = \frac{367}{760}\) atm.
Use the ideal gas law equation \(PV = nRT\) to solve for the number of moles \(n\). Rearrange the equation to \(n = \frac{PV}{RT}\).
Substitute the values of \(P\), \(V\), \(R\) (use \(0.0821\ \text{L}\cdot\text{atm}/\text{mol}\cdot\text{K}\)), and \(T\) into the equation and solve for \(n\).
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