Question #ef410

The first thing to do here is convert the volume from liters to cubic meters by using the fact that

#color(purple)(|bar(ul(color(white)(a/a)color(black)("1 L" = "1 dm"^3)color(white)(a/a)|)))" "# and #" "color(purple)(|bar(ul(color(white)(a/a)color(black)("1 m"^3 = 10^3 "dm"^3)color(white)(a/a)|)))#

Once you know the concentration of the gas in grams per cubic meters, you can convert it to pounds per cubic feet.

So, the concentration in grams per cubic meters will be

#3.5 * 10^(-6)"g"/color(red)(cancel(color(black)("L"))) * (1 color(red)(cancel(color(black)("L"))))/(1color(red)(cancel(color(black)("dm"^3)))) * (10^3color(red)(cancel(color(black)("dm"^3))))/"1 m"^3 = 3.5 * 10^(-3)"g m"^(-3)#

Now, the conversion factor that takes you from cubic meters to cubic feet can be calculated by

#"1 m"^3 = overbrace("1 m")^(color(blue)("= 3.28 ft")) xx overbrace("1 m")^(color(blue)("= 3.28 ft")) xx overbrace("1 m")^(color(blue)("= 3.28 ft"))#

#= "3.28 ft" xx "3.28 ft" xx "3.28 ft" = 3.28^3"ft"^3#

You will thus have

#3.5 * 10^(-3) color(red)(cancel(color(black)("g")))/color(red)(cancel(color(black)("m"^3))) * "1 lb"/(453.6color(red)(cancel(color(black)("g")))) * (1color(red)(cancel(color(black)("m"^3))))/(3.28^3"ft"^3) = color(green)(|bar(ul(color(white)(a/a)color(black)(2.2 * 10^(-7)"lb ft"^(-3))color(white)(a/a)|)))#

The answer is rounded to two sig figs.