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Chapter 5: Problem 80

At \(27^{\circ} \mathrm{C}, 10.0\) moles of a gas in a \(1.50-\mathrm{L}\) container exert a pressure of 130 atm. Is this an ideal gas?

Short Answer

Expert verified
To determine whether the gas is ideal or not, evaluate R from the ideal gas law equation with the given values. If the value matches the universal constant, then it's an ideal gas.

Step by step solution

01

Convert temperature to Kelvin

Convert the given \(27^{\circ}C\) to Kelvin by adding 273.15 \[ T = 27 + 273.15 = 300.15 K\]
02

Substitute given values into ideal gas law

Substitute the given values into the ideal gas law, \(PV = nRT\) and solve for R \[R = \frac{PV}{nT} = \frac{(130 \, \text{atm})(1.5 \, \text{L})}{(10.0 \, \text{mol})(300.15 \, \text{K})}\]
03

Evaluate R and determine if the gas is ideal

After evaluating the expression, if the calculated R-value is close to the known universal gas constant \((0.0821 \, \frac{L \cdot atm}{mol \cdot K})\), then the gas is ideal, otherwise it's not.

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