Question #3379d
1 Answer
Explanation:
This is a great example of a unit conversions problem.
Notice that the concentration of carbon monoxide is given in micrograms per cubic meter,
This means that you're going to have to use two conversion factors, one to take you from micrograms to grams
"1 g" = 10^6mu"g"1 g=106μg
and the other to take you meters to feet
"1 ft " = " 0.3048 m"1 ft = 0.3048 m
This means that
"1 ft"^3 = "1 ft" xx "1 ft" xx "1 ft"1 ft3=1 ft×1 ft×1 ft
"1 ft"^3 = "0.3048 m" xx "0.3048 m" xx "0.3048 m"1 ft3=0.3048 m×0.3048 m×0.3048 m
"1 ft"^3 = "0.028317 m"^31 ft3=0.028317 m3
The dimensions of the room will then help you find its volume. As you know, the volume of a rectangular prism is given by
color(blue)(|bar(ul(color(white)(a/a)V = l xx h xx wcolor(white)(a/a)|)))" " , where
One approach to have here is to convert the concentration of carbon monoxide from micrograms per cubic meter to grams per cubic feet by using the aforementioned conversion factors
48 color(red)(cancel(color(black)(mu"g")))/(color(red)(cancel(color(black)("m"^3)))) * (0.028317color(red)(cancel(color(black)("m"^3))))/("1 ft"^3) * "1 g"/(10^6color(red)(cancel(color(black)(mu"g")))) = 1.3592 * 10^(-6)"g ft"^(-3)
Next, use the dimensions of the room to find its volume.
V = "9.0 ft" xx "14.5 ft" xx "18.8 ft"
V = "2453.4 ft"^3
This means that the mass of carbon monoxide in this particular room will be
2453.4 color(red)(cancel(color(black)("ft"^3))) * overbrace((1.3592 * 10^(-6)"g")/(1color(red)(cancel(color(black)("ft"^3)))))^(color(purple)("equivalent to 48"mu"g m"^(-3))) = color(green)(|bar(ul(color(white)(a/a)3.3 * 10^(-3)"g"color(white)(a/a)|)))
The answer is rounded to two sig figs.
