For many purposes we can treat ammonia NH3 as an ideal gas at temperatures above its boiling point of −33.°C.Suppose the pressure on a 52.0g sample of ammonia gas at −15.0°C is tripled.Is it possible to change the temperature of the ammonia at the same time such that the volume of the gas doesn't change? yesnoIf you answered yes, calculate the new temperature of the gas. Round your answer to the nearest °C.
Question
For many purposes we can treat ammonia NH3 as an ideal gas at temperatures above its boiling point of −33.°C.Suppose the pressure on a 52.0g sample of ammonia gas at −15.0°C is tripled.Is it possible to change the temperature of the ammonia at the same time such that the volume of the gas doesn't change? yesnoIf you answered yes, calculate the new temperature of the gas. Round your answer to the nearest °C.
Solution
Yes, it is possible to change the temperature of the ammonia at the same time such that the volume of the gas doesn't change. This is because of the ideal gas law, which states that the pressure of a gas is directly proportional to its temperature if the volume and the amount of gas are kept constant.
To calculate the new temperature, we can use the ideal gas law equation:
P1/T1 = P2/T2
Where: P1 is the initial pressure T1 is the initial temperature P2 is the final pressure T2 is the final temperature
Given that the pressure is tripled, P2 = 3P1.
We are also given that the initial temperature T1 is -15.0°C. However, the ideal gas law requires temperatures to be in Kelvin, so we first convert this to Kelvin:
T1 = -15.0°C + 273.15 = 258.15 K
Substituting P2 = 3P1 and T1 = 258.15 K into the ideal gas law equation gives:
P1/258.15 K = 3P1/T2
Solving for T2 gives:
T2 = 3 * 258.15 K = 774.45 K
Converting this back to °C gives:
T2 = 774.45 K - 273.15 = 501.3°C
Rounding to the nearest °C gives a final temperature of 501°C.
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