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

Jan 17, 2017

$\text{510 g}$

#### Explanation:

The problem tells you that a 5% glucose solution has a specific gravity of $1.02$, which is a fancy way of saying that its density is approximately equal to

${\rho}_{\text{solution" = "1.02 g mL}}^{- 1}$

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 ${4}^{\circ} \text{C}$.

$\text{SG" = rho_"solution"/rho_"water}$

If we take water's maximum density to be equal to ${\text{1 g mL}}^{- 1}$, the density of the solution will indeed come out to be

${\rho}_{\text{solution" = "SG" * rho_"water}}$

${\rho}_{\text{solution" = 1.02 * "1 g mL"^(-1) = "1.02 g mL}}^{- 1}$

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

$500 \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{mL solution"))) * "1.02 g"/(1color(red)(cancel(color(black)("mL solution")))) = color(darkgreen)(ul(color(black)("510 g}}}}$

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

$\text{mass of 500 mL solution " = " 500 g}$