A container with a volume of 56.2 L holds helium at STP. The...

A container with a volume of 56.2 L holds helium at STP. The gas is compressed to $23.7 \mathrm{L}$ and 2.09 atm. To what must the temperature change $\left(^{\circ} \mathrm{C}\right)$ to satisfy the new volume and pressure?

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Key Concepts

Combined Gas Law

The combined gas law relates the pressure, volume, and temperature of a given amount of gas. It is derived by combining Boyle's law, Charles's law, and Gay-Lussac's law into a single equation: (P1 * V1) / T1 = (P2 * V2) / T2. This law is valuable when dealing with situations where a gas undergoes changes in multiple state variables simultaneously, as it allows one to solve for a missing variable when the other values change.

Temperature Conversion

Temperature conversion is a key concept when working with gas laws, because these laws require the absolute temperature scale (Kelvin) for calculations. Converting temperatures from degrees Celsius to Kelvin involves adding 273.15, ensuring that the proportional relationships between temperature and the other state variables remain accurate in the equations.

Standard Temperature and Pressure (STP)

Standard Temperature and Pressure (STP) are reference conditions frequently used in gas calculations, defined conventionally as a temperature of 0°C (273.15 K) and a pressure of 1 atm. Knowing STP conditions allows one to calculate or compare the behavior of gases under controlled, standardized conditions.

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