What is the temperature of 0.52 mol of gas at a pressure of 1.3 atm and a volume of 11.8 L?

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Identify the ideal gas law equation: \( PV = nRT \).

Rearrange the equation to solve for temperature \( T \): \( T = \frac{PV}{nR} \).

Substitute the given values into the equation: \( P = 1.3 \text{ atm} \), \( V = 11.8 \text{ L} \), \( n = 0.52 \text{ mol} \), and \( R = 0.0821 \text{ L atm mol}^{-1} \text{ K}^{-1} \).

Calculate the value of \( T \) using the substituted values.

Ensure the units are consistent and check the calculation for any errors.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Ideal Gas Law

The Ideal Gas Law is a fundamental equation in chemistry that relates the pressure, volume, temperature, and number of moles of an ideal gas. It is expressed as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature in Kelvin. This law allows us to calculate one of the variables if the others are known.

Units of Measurement

In the Ideal Gas Law, it is crucial to use consistent units. Pressure is typically measured in atmospheres (atm), volume in liters (L), and temperature in Kelvin (K). To convert Celsius to Kelvin, add 273.15. Ensuring that all units are compatible is essential for accurate calculations.

Gas Constant (R)

The gas constant (R) is a proportionality constant in the Ideal Gas Law, with a value of 0.0821 L·atm/(K·mol) when using atm for pressure and liters for volume. This constant allows for the conversion between the different units in the equation and is essential for solving for temperature or any other variable in the context of gas behavior.

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