Q. 2.119 - An Introduction to General, Organic, and Biological Chemistry

Question

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

Step-by-Step Solution

Answer

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

Step 1 : 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

Step 2 : 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 $0.74 \mathrm{g}/\mathrm{mL}$, and the volume is $1.50 \mathrm{L}$. By converting the units of volume from $\mathrm{L}$ 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.

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

Step 3 : Explanation

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

$Density =\frac{mass of subs\tan ce}{volume of subs\tan ce}$

We get by rearranging the mass to solve the problem.

 $mass of subs\tan ce =Density\times volume of subs\tan ce$

$$\begin{gathered} mass of subs\tan ce =0.74 \frac{g }{c{m}^3} \times 1,500 \mathrm{c}{m}^3 \\ =1,110 g \end{gathered}$$

The mass of gasoline is found as $1110 \mathrm{g}$

Step 4: 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 $0.92 \mathrm{g}/{\mathrm{cm}}^3$.

Hence, the volume of olive oil is given as:

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

$=1200 {\mathrm{cm}}^3$

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