Which flask contains gas of molar mass 30, and which contains gas of molar mass 60?
Suppose you are given two 1-L flasks and told that one contains a gas of molar mass 30, the other a gas of molar mass 60, both at the same temperature. The pressure in flask A is X kPa, and the mass of gas in the flask is 1.2 g. The pressure in flask B is 0.5 X kPa, and the mass of gas in that flask is 1.2 g.
Suppose you are given two 1-L flasks and told that one contains a gas of molar mass 30, the other a gas of molar mass 60, both at the same temperature. The pressure in flask A is X kPa, and the mass of gas in the flask is 1.2 g. The pressure in flask B is 0.5 X kPa, and the mass of gas in that flask is 1.2 g.
1 Answer
Here's what I got.
Explanation:
!! QUICK ANSWER !!
The trick here is to realize that
- pressure is directly proportional to the number of moles of gas present in each flask
- the number of moles is inversely proportional to the molar mass of the gas
Pressure is directly proportional to the number of moles of gas, which means that a pressure that is twice as high corresponds to twice as many moles of gas present in the flask.
Therefore, flask A contains twice as many moles of gas as flask B. Now, the heavier gas will contain fewer moles in the same mass.
The two samples have the same mass, but flask A contains twice as many moles as flask B, which can only mean that the gas present in flask A has a molar mass of
Therefore,
#"Flask A " -> " 30 g mol"^(-1)#
#"Flask B " -> " 60 g mol"^(-1)#
!! DETAILED EXPLANATION !!
The problem tells you that the two flasks have the same volume, let's say
This means that if you start from the ideal gas law equation
where
#P# - the pressure of the gas
#V# - the volume it occupies
#n# - the number of moles of gas
#R# - the universal gas constant
#T# - the absolute temperature of the gas
you can say that you have
#P_A * V = n_A * R * T -># for the gas present in flask A
#P_b * V = n_B * R * T -># for the gas present in flask B
Divide these two equations to find a relationship between the pressure of the two gases and the number of moles of gas present in each flask
#(P_A * color(red)(cancel(color(black)(V))))/(P_B * color(red)(cancel(color(black)(V)))) = (N_A * color(red)(cancel(color(black)(R))) * color(red)(cancel(color(black)(T))))/(n_B * color(red)(cancel(color(black)(R))) * color(red)(cancel(color(black)(T)))) implies P_A/P_B = n_A/n_B#
Now, you know that the pressure in flask A, given as
This means that the ratio between the number of moles of gas present in each flask will be
#(color(red)(cancel(color(black)("X")))color(red)(cancel(color(black)("kPa"))))/(1/2 * color(red)(cancel(color(black)("X"))) color(red)(cancel(color(black)("kPa")))) = n_A/n_B implies n_A/n_B =2#
This is equivalent to
#color(purple)(|bar(ul(color(white)(a/a)color(black)(n_A = 2 * n_B)color(white)(a/a)|)))" " " "color(orange)("(*)")#
You now know that flask A contains twice as many moles of gas as flask B.
Now, you know that the two gases have the same mass, given as
This is the case because
#n_A = (1.2 color(red)(cancel(color(black)("g"))) )/(M_A color(red)(cancel(color(black)("g"))) "mol"^(-1)) = 1.2/M_Acolor(white)(a)"moles"#
#n_B = (1.2 color(red)(cancel(color(black)("g"))))/(M_B color(red)(cancel(color(black)("g"))) "mol"^(-1)) = 1.2/M_B color(white)(a)"moles"#
According to equation
#color(red)(cancel(color(black)(1.2)))/M_A = 2 * color(red)(cancel(color(black)(1.2)))/M_B implies color(green)(|bar(ul(color(white)(a/a)color(black)(M_B = 2 * M_A)color(white)(a/a)|)))#
This means that flask A contains the gas with the molar mass of
Once again,
#"Flask A " -> " 30 g mol"^(-1)#
#"Flask B " -> " 60 g mol"^(-1)#