# A 5% glucose solution has a specific gravity of 1.02. What is the mass of 500 mL of glucose solution?

##### 1 Answer

#### Explanation:

The problem tells you that a **density** is approximately equal to

#rho_"solution" = "1.02 g mL"^(-1)#

That is the case because **specific gravity** is calculated by dividing the density of a solution by the **maximum density of water**, which occurs when water has a temperature of

#"SG" = rho_"solution"/rho_"water"#

If we take water's maximum density to be equal to

#rho_"solution" = "SG" * rho_"water"#

#rho_"solution" = 1.02 * "1 g mL"^(-1) = "1.02 g mL"^(-1)#

Now that you know the density of the solution, you can use it to find the mass of the sample

#500 color(red)(cancel(color(black)("mL solution"))) * "1.02 g"/(1color(red)(cancel(color(black)("mL solution")))) = color(darkgreen)(ul(color(black)("510 g")))#

I'll leave the answer rounded to two **sig figs**, but keep in mind that you only have one significant figure for the volume of the sample and for the percent concentration of the solution, so the answer *should* be given as

#"mass of 500 mL solution " = " 500 g"#