Question

solve the following problem:
what pressure is required to contain 0.23 moles of nitrogen gas in a 4.2 l container at a temperature of 20°c?

Explanation:

Step1: Convert temperature to Kelvin

The ideal gas law uses temperature in Kelvin. The conversion formula is \(T(K)=T(^{\circ}C)+273.15\). Given \(T = 20^{\circ}C\), then \(T=(20 + 273.15)K=293.15K\).

Step2: Recall the ideal gas law

The ideal gas law is \(PV = nRT\), where \(P\) is pressure, \(V\) is volume, \(n\) is the number of moles, \(R\) is the ideal gas constant (\(R=0.0821\ L\cdot atm/(mol\cdot K)\)), and \(T\) is temperature. We need to solve for \(P\), so \(P=\frac{nRT}{V}\).

Step3: Substitute the values

We are given \(n = 0.23\ mol\), \(V=4.2\ L\), \(R = 0.0821\ L\cdot atm/(mol\cdot K)\), and \(T = 293.15K\).

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Answer:

\(1.32\ atm\)