Yesterday, Jason had a sample of helium indoors (T = 23oC) in a sealed container, with a pressure of 760 mm Hg. He got bored and took the container outside, where the temperature was a blistering 35oC. He calculated the new pressure to be 750 mm Hg. Jason knew that this answer was not correct because:
TK = ToC + 273.15
Equal volumes of gas have the same number of moles.
P is proportional to n
P is proportional to T
He forgot to convert his temperature to K and the pressure should have decreased even more.
I'm a little confused by the answers. #1 is a correct statement in that Kelvin T = 273.15 + Celsius.
#2 is a correct statement, also.
#3 is a correct statement.
#4 is a correct statement.
We know #5 is not the answer because the pressure will go up (not down) as the T increases.
I suppose we must make a guess as to which of the correct statements is the answer. My best guess is p is proportional to T (answer #4). Check my thinking. Jason's calculated produced a lower number but we know increased T increases P BECAUSE pressure is directly proportional to T.
The correct answer is: He forgot to convert his temperature to K and the pressure should have decreased even more.
To understand why this is the correct answer, let's break it down:
1. TK = ToC + 273.15: This equation is used to convert temperature from degrees Celsius (oC) to Kelvin (K). Since the variables in the ideal gas equation need to be in Kelvin, temperature should always be converted to K before performing any calculations.
2. Equal volumes of gas have the same number of moles: This is Avogadro's law, which states that equal volumes of gases at the same temperature and pressure contain an equal number of molecules. This means the number of moles (n) of the gas remains constant during the process.
3. P is proportional to n: According to the ideal gas law (PV = nRT), pressure (P) is directly proportional to the number of moles (n). Since the number of moles remains constant, the pressure should also remain constant, provided the other variables (volume and temperature) are held constant.
4. P is proportional to T: The ideal gas law also states that pressure is directly proportional to temperature (P ∝ T), assuming other variables are constant. Therefore, if the temperature increases while the other variables stay the same, the pressure would increase as well.
From the given information, we can conclude that if the temperature increased from 23oC to 35oC, then the pressure should have increased as well. However, Jason calculated the new pressure to be 750 mm Hg, which is lower than the initial pressure of 760 mm Hg. This implies that the calculated value is incorrect.
The reason for the incorrect calculation is stated in the correct answer: Jason forgot to convert the temperature to Kelvin. It's crucial to use the Kelvin scale for temperature in gas law calculations because it directly influences pressure. By converting the temperature, Jason would have obtained a higher value, resulting in a decrease in pressure, which is the expected outcome when the temperature increases.