A 0.50 L container is occupied by nitrogen at a pressure of...

A $0.50 \mathrm{~L}$ container is occupied by nitrogen at a pressure of 800 torr and a temperature of $0^{\circ} \mathrm{C}$. The container can only withstand a pressure of $3.0 \mathrm{~atm} .$ What is the highest temperature $\left({ }^{\circ} \mathrm{C}\right)$ to which the container may be heated? (a) 505 (b) 450 (c) 625 (d) 560

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Key Concepts

Ideal Gas Law

The ideal gas law, expressed as PV = nRT, relates the pressure, volume, temperature, and number of moles of a gas. In many thermodynamic problems, this law is used to understand how changes in one variable affect the others when the gas behaves ideally.

Constant Volume Process

A constant volume process is one in which the volume of the gas does not change. Under these conditions, any change in temperature directly corresponds to a proportional change in pressure, as described by the relation P/T = constant, provided the number of moles remains unchanged.

Temperature Conversion to Absolute Scale

Temperature in thermodynamics is used in its absolute form, typically Kelvin, to make use of the proportional relationships in the ideal gas law. This requires converting Celsius to Kelvin by adding 273.15, ensuring that calculations involving ratios, such as P1/T1 = P2/T2, are correctly applied.

Unit Conversion for Pressure

Proper unit conversion for pressure is crucial when using the gas laws. This involves converting units like torr to atm or other consistent pressure units to ensure accuracy in calculations, maintaining consistency across all parameters involved in the computation.

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