A 48.3-mL sample of gas in a cylinder is warmed from 22 °C to 87 °C. What is its volume at the final temperature?

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Identify the initial and final temperatures and convert them from Celsius to Kelvin. Use the formula: \( T(K) = T(°C) + 273.15 \).

Apply Charles's Law, which states that \( \frac{V_1}{T_1} = \frac{V_2}{T_2} \), where \( V_1 \) and \( T_1 \) are the initial volume and temperature, and \( V_2 \) and \( T_2 \) are the final volume and temperature.

Substitute the known values into the equation: \( V_1 = 48.3 \text{ mL} \), \( T_1 = 22 + 273.15 \text{ K} \), and \( T_2 = 87 + 273.15 \text{ K} \).

Rearrange the equation to solve for \( V_2 \): \( V_2 = V_1 \times \frac{T_2}{T_1} \).

Calculate \( V_2 \) using the rearranged equation to find the final volume of the gas at 87 °C.

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주요 개념

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Charles's Law

Charles's Law states that the volume of a gas is directly proportional to its temperature (in Kelvin) when pressure is held constant. This relationship can be expressed mathematically as V1/T1 = V2/T2, where V is volume and T is temperature. Understanding this law is essential for solving problems involving changes in temperature and volume of gases.

Temperature Conversion

In gas law calculations, temperatures must be expressed in Kelvin rather than Celsius. The conversion from Celsius to Kelvin is done by adding 273.15 to the Celsius temperature. This step is crucial because gas laws are based on absolute temperature, which affects the behavior of gases.

Ideal Gas Behavior

The ideal gas law describes the behavior of an ideal gas, which follows the relationships defined by pressure, volume, temperature, and the number of moles of gas. While real gases may deviate from ideal behavior under certain conditions, understanding this concept helps in applying gas laws effectively and predicting how gases will respond to changes in temperature and volume.