Question #b51d7
1 Answer
Explanation:
In order to be able to determine the identity of the gas, you must figure out its molar mass.
Since you know the mass of the sample, you can use the ideal gas law equation to find the number of moles present in the sample. Dividing these two values will give you the molar mass of the gas.
So, the ideal gas law equation looks like this
#color(blue)(PV = nRT)" "# , where
Now, you need to pay attention to the units used in the expression of the ideal gas constant and make sure that your units match those units.
You need to have the pressure expressed in atm, the volume in liters, and the temperature in Kelvin, so use the conversion factors
#"1 L" = 10^3"mL"#
#"1 atm " = "760 torr"#
Rearrange the ideal gas law equation to solve for
#PV = nRT implies n = (PV)/(RT)#
#n = (943/760 color(red)(cancel(color(black)("atm"))) * 275 * 10^(-3)color(red)(cancel(color(black)("L"))))/(0.0821(color(red)(cancel(color(black)("atm"))) * color(red)(cancel(color(black)("L"))))/("mol" * color(red)(cancel(color(black)("K")))) * (273.15 + 25.5)color(red)(cancel(color(black)("K"))))#
#n = "0.01392 moles"#
The molar mass of the gas will tell you the mass of one mole of the gas. Since you know that
#1color(red)(cancel(color(black)("mole"))) * "2.22 g"/(0.01392color(red)(cancel(color(black)("moles")))) = "159.5 g"#
This means that the molar mass of the gas is equal to
The only gas on your list that comes close to having this molar mass is bromine,
All the other options have significantly smaller molar masses, so bromine will be your answer.