Question #0f7fb
1 Answer
Explanation:
The idea here is that you first need to sue the ideal gas law to find how many moles of oxygen gas you have in that sample, then use the combined gas law to find the volume of the sample at STP conditions.
So, start by calculating the number of moles of oxygen gas you have in that sample - do not forget to convert the pressure from torr to atm, the volume from lililiters to liters, and the temperature to Kelvin
PV = nRT implies n = (PV)/(RT)PV=nRT⇒n=PVRT
n = (760/738.2color(red)(cancel(color(black)("atm"))) * 380 * 10^(-3)color(red)(cancel(color(black)("L"))))/(0.082(color(red)(cancel(color(black)("atm"))) * color(red)(cancel(color(black)("L"))))/("mol" * color(red)(cancel(color(black)("K")))) * (273.15 + 25)color(red)(cancel(color(black)("K")))) = "0.0160 moles O"""_2
Now, STP conditions imply a pressure of
P_1 * V_1 = nR * T_1 -> for your initial conditions
P_2 * V_2 = nR * T_2 -> for STP conditions
Divide these two equations to get
(P_1 * V_1)/(P_2 * V_2) = (color(red)(cancel(color(black)(n * R))) * T_1)/(color(red)(cancel(color(black)(n * R))) * T_2)
which is equivalent to the combined gas law form
(P_1V_1)/T_1 = (P_2V_2)/T_2
Rearrange this equation to solve for
V_2 = P_1/P_2 * T_2/T_1 * V_1
This means that you have
V_2 = (760/738.2color(red)(cancel(color(black)("atm"))))/(100/101.325color(red)(cancel(color(black)("atm")))) * (273.15color(red)(cancel(color(black)("K"))))/((273.15 + 25)color(red)(cancel(color(black)("K")))) * 380 * 10^(-3) "L"
V_2 = "0.3631668 L"
To get the molar volume of oxygen gas at STP, divide this value by the number of moles you have in the sample
V_"molar STP" = V_"STP"/n
V_"molar STP" = "0.3631668 L"/"0.0160 moles" = "22.697 L/mol"
I'' leave the answer rounded to three sig figs
V_"molar STP" = color(green)("22.7 L/mol")
SIDE NOTE Many online sources and textbooks still define STP conditions as a pressure of 1 atm and a temperature of
That is a very old definition of STP conditions that will produce a molar volume of 22.4 L. If you are supposed to use those conditions for pressure and temperature, simply redo the calculations using 1 atm instead of 100 kPa.