Question

The specific gravity of gold is 19.3. What is the length of one side of a 0.4 kilograms cube of solid gold, in units of inches?

Answer 1

Specif gravity = density of the material / density of water

density of the material = specific gravity * density of water

density of gold = 19.3 * 1 g/mL = 19.3 g/mL

density = mass / volume ==> Volume = mass / density

Volume = 0.4 kg * 1000 g/kg / 19.3 g/mL = 20.725 mL

Length of one side of the cube = $\sqrt[3]{20.725 {cm}^{3} }$ = 2.75 cm

Pass cm to inches
2.75 cm * 1 inch / 2.54 cm = 1.08 inch

Answer 2

The length of the solid cube of gold is $\boxed{{\text{1}}{\text{.08 in}}}$

Further explanation:

Specific gravity:

Specific gravity is defined as the ratio of the density of the substance to the density of water. It is a unitless quantity as it includes the ratio of two similar quantities.

The formula to calculate specific gravity of gold is as follows:

${\text{Specific gravity of gold}}=\frac{{{\text{Density of gold}}}}{{{\text{Density of water}}}}$           …… (1)

Density is considered as a characteristic property of the substance. It is an intensive property. It is defined as the mass per unit volume. It is generally represented by $\rho$ .

The formula to calculate the density of gold is,

$\text{Density of gold}(\rho)=\dfrac{\text{Mass of gold(M)}}{\text{Volume of gold(V)}}$           …… (2)

Rearrange equation (1) to calculate the density of gold.

${\text{Density of gold}}=\left({{\text{Specific gravity of gold}}}\right)\left({{\text{Density of water}}}\right)$           …… (3)

The specific gravity of gold is 19.3.

The density of water is 1 g/mL.

Substitute these values in equation (2).

$\align{{\text{Density of gold}}&=\left({{\text{19}}{\text{.3}}}\right)\left({\frac{{{\text{1 g}}}}{{{\text{1 mL}}}}}\right)\cr&=19.3\;{\text{g/mL}}\cr}$

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

${\text{Volume of gold}}=\frac{{{\text{Mass of gold}}}}{{{\text{Density of gold}}}}$            …… (4)

The mass of gold is 0.4 kg. Firstly, we have to convert the mass of gold from kg to g. The conversion factor for this is as follows:

${\text{1 kg}}= \text{1}}{{\text{0}}^{\text{3}}}{\text{ g}}$

So the mass of gold is calculated as follows:

$\align{{\text{Mass of gold}}&=\left({{\text{0}}{\text{.4 kg}}}\right)\left({\frac{{{\text{1}}{{\text{0}}^{\text{3}}}{\text{ g}}}}{{{\text{1 kg}}}}}\right)\cr&=400\;{\text{g}}\cr}$

Mass of gold is 400 g.

Density of gold is 19.3 g/mL.

Substitute these values in equation (4).

$\align{{\text{Volume of gold}}&=\left({{\text{400 g}}}\right)\left({\frac{{1\;{\text{mL}}}}{{{\text{19}}{\text{.3 g}}}}}\right)\cr&={\text{20}}{\text{.725 mL}}\cr}$

The formula to calculate the volume of a gold cube is as follows:

${\text{Volume of gold cube}}={\left({{\text{Length of gold cube}}}\right)^3}$           …… (5)

Rearrange equation (5) to calculate the length of the gold cube.

${\text{Length of gold cube}}=\root3\of{{\text{Volume of gold cube}}}$           …… (6)

The volume of gold is 20.725 mL or ${\text{20}}{\text{.725 c}}{{\text{m}}^{\text{3}}}$ .

Substitute this value in equation (6).

$\align{{\text{Length of gold cube}}&=\root3\of{{\text{20}}{\text{.725 c}}{{\text{m}}^3}}\cr&=2.7468\;{\text{cm}}\cr&\approx{\text{2}}{\text{.75 cm}}\cr}$

The conversion factor required to convert the length of the gold cube from cm to inches is as follows:

${\text{1 cm}}=0.3937\;{\text{in}}$

So the length of the gold cube is calculated as follows:

$\align{{\text{Length of gold cube}}&=\left({{\text{2}}{\text{.75 cm}}}\right)\left({\frac{{{\text{0}}{\text{.3937 in}}}}{{{\text{1 cm}}}}}\right)\cr&={\text{1}}{\text{.082675 in}}\cr&\approx{\bf{1}}{\bf{.08 in}}\cr}$

Learn more:

1. Calculate the molar mass of phenol: brainly.com/question/5671083

2. Find the final pressure of the system: brainly.com/question/6340739

Answer details:

Grade: High School

Subject: Chemistry

Chapter: Density

Keywords: specific gravity, density, volume of gold cube, length of gold cube, inches, cm, 1.08 in, 2.75 cm, 19.3, 19.3 g/mL, density of gold, density of water, 1 g/mL, conversion factor.