A 50.0 mL urine sample has a mass of 50.7 g. What is the specific gravity of the urine?

1 Answer
Nov 8, 2016




The specific gravity of a substance, #"SG"#, is simply the ratio between that substance's density and the density of a reference substance, which is usually water at #4^@"C"#, the temperature at which its density is maximum.

So right from the start, the fact that specific gravity is a ratio of two densities should let you know that you're looking for a unitless quantity.

In your case, the specific gravity of urine will be

#"SG"_ "urine" = rho_"urine"/rho_"water"#

Use the mass and volume of the sample to calculate its density, which is essentially the mass of *one unit of volume of a given substance

#1 color(red)(cancel(color(black)("mL"))) * "50.7 g"/(50.0color(red)(cancel(color(Black)("mL")))) = "1.014 g"#

This means that urine has a density of #"1.014 g mL"^(-1)#, i.e. every milliliter of urine has a mass of #"1.014 g"#.

Now, water has a maximum density of #"0.999975 g mL"^(-1)# at #4^@"C"#, so use this value to find the specific gravity of urine

#"SG"_ "urine" =(1.014 color(red)(cancel(color(black)("g mL"^(-1)))))/(0.999975color(red)(cancel(color(black)("g mL"^(-1))))) = color(green)(bar(ul(|color(white)(a/a)color(black)(1.01)color(white)(a/a)|))) #

The answer is rounded to three sig figs.