What is the molar mass of a gas that has a density of 1.02 g/L at 0.990 atm pressure and 37°C?
1 Answer
Explanation:
Your starting point here will be the ideal gas law equation
#color(blue)(|bar(ul(color(white)(a/a)PV = nRTcolor(white)(a/a)|)))" "# , where
Now, you will have to manipulate this equation in order to find a relationship between the density of the gas,
You know that the molar mass of a substance tells you the mass of exactly one mole of that substance. This means that for a given mass
#color(blue)(|bar(ul(color(white)(a/a)color(black)(M_M = m/n)color(white)(a/a)|)))" " " "color(orange)((1))#
Similarly, the density of the substance tells you the mass of exactly one unit of volume of that substance.
This means that for the mass
#color(blue)(|bar(ul(color(white)(a/a)color(black)(rho = m/V)color(white)(a/a)|)))" " " "color(orange)((2))#
Plug equation
#PV = m/M_M * RT#
Rearrange to get
#PV * M_M = m * RT#
#P * M_M = m/V * RT#
#M_M = m/V * (RT)/P#
Finally, use equation
#M_M = rho * (RT)/P#
Convert the temperature of the gas from degrees Celsius to Kelvin then plug in your values to find
#M_M = 1.02 "g"/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 + 37)color(red)(cancel(color(black)("K"))))/(0.990color(red)(cancel(color(black)("atm"))))#
#M_M = color(green)(|bar(ul(color(white)(a/a)color(black)("26.3 g mol"^(-1))color(white)(a/a)|)))#
I'll leave the answer rounded to three sig figs.