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At what temperature in °C does 0.750 mol of an ideal gas occupy a volume of 35.9 L at a pressure of 1.13 atm?

(Use the ideal gas constant: [tex] R = 0.0821 \, \text{atm} \cdot \text{L/mol} \cdot \text{K} [/tex])

Answer :

Answer:

386°C

Explanation:

The ideal gas law allows us to solve for different values of a gas.

Ideal Gas Law

In order to do ideal gas calculations, we make the assumption that gas behaves ideally. This means that gases move in completely straight lines, have perfectly elastic collisions, experience no IMFs (intermolecular forces), and have no volume. When we assume these characteristics, we get the equation:

  • PV = nRT

In this equation, P is pressure, V is volume, n is moles, R is the gas constant, and T is temperature. It is important to note that temperature is always given in Kelvin for the ideal gas law.

Solving For T

To solve for T, all we need to do is plug in the values we were given. The question states:

  • P = 1.13 atm
  • V = 35.9 L
  • n = 0.750 mol
  • R = 0.0821atm*L/mol*K

Now we just need to solve for T. For clarity, I will leave units out of this calculation.

  • 1.13 * 35.9 = 0.750 * 0.0821 * T
  • T ≈ 658.82 K

This means the temperature is about 658.82 Kelvin. Rounded for sig figs, this is 659K. However, the question asks for Celsius. So, we need to convert. To convert from Kelvin to Celsius, subtract 273.

  • 659K = 386°C

The gas is at 386°C.

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Rewritten by : Jeany

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