# Question a54ac

Jan 10, 2017

${\text{0.9637 g mL}}^{- 1}$

#### Explanation:

You know that in order to find the density of a substance, you need to know two things

• the volume of a given sample of said substance
• the mass of this sample

The problem tells you that $\text{10.00 mL}$ of substance $\text{A}$ are being added to the empty flask, so right from the start you know the volume of the sample.

Now, in order to find its mass, you must use the mass of the empty flask and the mass of the flask + sample. You can say that after you fill the empty flask with the sample of substance $\text{A}$, you have

$\textcolor{b l u e}{\underline{\textcolor{b l a c k}{{m}_{\text{flask + sample" = m_"flask" + m_"sample}}}}}$

This means that

${m}_{\text{sample" = m_"flask + sample" - m_"flask}}$

In your case, this will give you

${m}_{\text{sample" = "24.461 g" - "14.824 g}}$

${m}_{\text{sample" = "9.637 g}}$

So now you know the volume of the sample and its mass. In order to find its density, $\rho$, divide the two values

rho = "9.637 g"/"10.00 mL" = color(darkgreen)(ul(color(black)("0.9637 g mL"^(-1))))

The answer is rounded to four sig figs.

Notice that this is equivalent to determining the mass of one unit of volume, which would be $\text{1 mL}$, by using the mass and volume of the sample

1 color(red)(cancel(color(black)("mL"))) * overbrace("9.637 g"/(10.00color(red)(cancel(color(black)("mL")))))^(color(blue)("what you know about the sample")) = "0.9637 g"#

This means that the density of the substance, which by definition is the mass of one unit of volume of said substance, will once again be

$\rho = \textcolor{\mathrm{da} r k g r e e n}{\underline{\textcolor{b l a c k}{{\text{0.9637 g mL}}^{- 1}}}} \to$ this tells you that every $\text{1 mL}$ of substance $\text{A}$ has a mass of $\text{0.9637 g}$