What is the density of acetylene gas measured at pressure of 0.75 atm and temperature of 250°C?
1 Answer
Explanation:
Your strategy here will be to use the molar mass of acetylene,
So, the ideal gas law equation looks like this
#color(blue)(PV = nRT)" "# , where
Now, since you don't know how many moles of acetylene you have, you will have to work around it using the definition of molar mass.
A substance's molar mass tells you what the mass of one mole of that substance is. You can thus write molar mass,
#color(blue)(M_M = m/n)" "# , where
This means that you can express the number of moles,
#M_M = m/n implies n = m/M_M#
Plug this into the ideal gas law equation to get
#PV = m/M_M * RT" " " "color(red)(("*"))#
Now, density,
#color(blue)(rho = m/V)" "# , where
Rearrange equation
#P * M_M = overbrace(m/V)^(color(blue)(=rho)) * RT#
This means that you have
#rho * RT = P * M_M implies rho = (P * M_M)/(RT)#
Acetylene has a molar mass of
#rho = (0.75 color(red)(cancel(color(black)("atm"))) * 26.037"g"/color(red)(cancel(color(black)("mol"))))/(0.0821(color(red)(cancel(color(black)("atm"))) * "L")/(color(red)(cancel(color(black)("mol"))) * color(red)(cancel(color(black)("K")))) * (273.15 + 250)color(red)(cancel(color(black)("K")))) = "0.4547 g/L"#
Rounded to two sig figs, the number of sig figs you have for the temperature and pressure of the gas, the answer will be
#rho = color(green)("0.45 g/L")#