Question

A drop of gasoline has a mass of 22 mg and a density of 0.754 g/cm3. What is its volume in cubic centimeters?

Answer 1

The volume of gasoline (in cubic centimeters) is $\boxed{0.029\;\text{cm}^3}$.

Further Explanation:

Density is defined as the mass of the substance per unit volume of the substance. It is denoted by $\rho$. It is generally expressed in the units of grams per cubic centimeter $(\text{g/cm}^3)$. The formula to calculate the density of a substance is as follows:

$\rho=\dfrac{\text{M}}{\text{V}}$  

Here,

$\rho$ is the density of the substance.

M is the mass of the substance.

V is the volume of the substance.

The formula to calculate the density of gasoline is as follows:

$\text{Denstiy of gasoline}=\dfrac{\text{Mass of gasoline}}{\text{Volume of gasoline}}$                                                             …… (1)

Rearrange equation (2) to calculate the volume of gasoline.

$\text{volume of gasoline}=\dfrac{\text{Mass of gasoline}}{\text{Density of gasoline}}$             …… (2)                                              

The mass of gasoline is 22 mg. This is to be converted into g. The conversion factor for this is,

$1\;\text{mg}=10^{-3}\text{g}$  

Therefore the mass of gasoline can be calculated as follows:

 $\begin{aligned}{\text{Mass of gasoline}}&= \left( {22{\text{ mg}}} \right)\left( {\frac{{{{10}^{ - 3}}{\text{ g}}}}{{1{\text{ mg}}}}} \right)\\&= 0.022{\text{ g}} \\ \end{aligned}$

The mass of gasoline is 0.022 g.

The density of gasoline is $0.754\;\text{g/cm}^3$.

Substitute these values in equation (2).

 $\begin{aligned}\text{Volume of gasoline}&=\frac{0.022\;\text{g}}{0.754\;\text{cm}^3}\\&=0.029\text{cm}^3\\\end{aligned}$

Therefore the volume of gasoline is $0.029\;\text{cm}^3$.

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Answer details:

Grade: Middle School

Chapter: Density

Subject: Chemistry

Keywords: density, mass, volume, 22 mg, 0.022 g, 0.029 cm^3, volume of gasoline, mass of gasoline, density of gasoline, $0.754 \;\text{g/cm}^3, g$, conversion factor.

Answer 2

Answer:

volume = 0.029 cm³

Explanation:

We are given that:

mass = 22 mg

We know that:

1 mg = 0.001 grams

This means that:

mass = 22 mg = 0.022 grams

We are also given that:

density = 0.754 g/cm³

Density is calculated using the following rule:

$Density=\frac{mass}{volume}$

Rewrite the equation to solve for volume:

$volume = \frac{mass}{density}$

Now, substitute with the values we have:

$volume = \frac{0.022}{0.754} = 0.029 cm^3$

Hope this helps :)