Question

A 20.0 L gas at 150. Celsius was cooled to 15.0 Celsius. What will be the new volume of the gas if the number of moles and pressure of the gas remain unchanged

Answer 1

Applying Charles's Law to a gas that is cooled from 150 Celsius to 15.0 Celsius with constant pressure and moles, the volume decreases from 20.0 L to approximately 13.63 L.

Step-by-step explanation:

The question relates to the behavior of gases under different temperatures while keeping the pressure and the number of moles constant. This is a classic application of Charles's Law, which states that the volume of a gas is directly proportional to its temperature (in Kelvin), when pressure and number of moles remain unchanged. Given that a 20.0 L gas at 150 Celsius is cooled to 15.0 Celsius, we first need to convert these temperatures to Kelvin. The temperature conversion from Celsius to Kelvin is:

• 
  
• T(K) = T(C) + 273.15

For the initial temperature:

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• 150°C + 273.15 = 423.15 K

For the final temperature:

• 
  
• 15.0°C + 273.15 = 288.15 K

Now, we apply Charles's Law:

• 
  
• V1/T1 = V2/T2

Plugging in the values, we get:

• 
  
• (20.0 L) / (423.15 K) = V2 / (288.15 K)

When you solve for V2, the final volume:

• 
  
• V2 = (20.0 L)(288.15 K) / (423.15 K)
• 
  
• V2 ≈ 13.63 L

Therefore, the new volume of the gas after being cooled to 15.0 Celsius, with the pressure and number of moles remaining unchanged, would be approximately 13.63 liters.