Question

How many milliliters of olive oil has the same mass as $1.90\mathrm{L}$ of gasoline (see Table 2.8) ? (2,7)

Short answer

Olive oil has the same mass as gasoline and has a volume of $1,200{\mathrm{cm}}^3$.

Step-by-step solution

Given information

The given is the elements olive oil and gasoline

The objective is to determine how many milliliters of olive oil has same mass as gasoline

Explanation 

It's time to calculate the volume of olive oil, which has the same mass as gasoline.

The density expression is well-known.

$\text{Density}=\frac{\text{mass of substance}}{\text{volume of substance}}$

The density of gasoline is localid="1653606146033" $0.74\mathrm{g}/\mathrm{mL}$, and the volume is localid="1653606154957" $1.50\mathrm{L}$. By converting the units of volume from localid="1653606135246" $\mathrm{L}$to $\mathrm{mL}$, we have

$1\mathrm{L}=1,000\mathrm{mL}$

and

$1\mathrm{mL}=1{\mathrm{cm}}^3$

Hence, we get

$1\mathrm{L}=1,000{\mathrm{cm}}^3\text{.}$

We have achieved this by employing the appropriate conversion factor.

$1.50\mathrm{L}\times \frac{1,000\mathrm{mL}}{1\mathrm{L}}\times \frac{1{\mathrm{cm}}^3}{1\mathrm{mL}}=1,500{\mathrm{cm}}^3$

We may convert the unit of volume to the density of gasoline by converting the unit of volume to the density of gasoline.

$0.74\frac{\mathrm{g}}{\mathrm{mL}}\times \frac{1\mathrm{mL}}{1{\mathrm{cm}}^3}=0.74\frac{\mathrm{g}}{{\mathrm{cm}}^3}$

Explanation 

We get $1500{\mathrm{cm}}^3$by substituting$0.74g/c{m}^3$for density and $0.74\mathrm{g}/{\mathrm{cm}}^3$for volume in the density expression.

$Density=\frac{massofsubs\tan ce}{volumeofsubs\tan ce}$

We get by rearranging the mass to solve the problem.

$massofsubs\tan ce=Density\times volumeofsubs\tan ce$

localid="1653887014660" $$\begin{gathered} massofsubs\tan ce=0.74\frac{g}{c{m}^3}\times 1,500\mathrm{c}{m}^3 \\ =1,110g \end{gathered}$$

The mass of gasoline is found as localid="1653058178820" $1110\mathrm{g}$

Density of olive oil

The density of olive oil is $0.92\mathrm{g}/\mathrm{mL}$. By converting the unit of volume in the density of olive oil,

We have

$0.92\frac{\mathrm{g}}{\mathrm{mL}}\times \frac{1\mathrm{mL}}{1{\mathrm{cm}}^3}=0.92\frac{\mathrm{g}}{{\mathrm{cm}}^3}$

The mass of olive oil is the same as gasoline's mass. As a result, the volume of olive oil is $1,110\mathrm{g}$, and the density is localid="1653058600362" $0.92\mathrm{g}/{\mathrm{cm}}^3$.

Hence, the volume of olive oil is given as:

$\text{volume of substance}=\frac{1,110\mathrm{g}}{0.92\frac{\mathrm{g}}{{\mathrm{cm}}^3}}$

localid="1653059082547" $=1200{\mathrm{cm}}^3$

As a result, the volume of olive oil that has the same mass as gasoline is localid="1653059115948" $1,200{\mathrm{cm}}^3$.