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The density of gold is \(19.3 \mathrm{~g} / \mathrm{cm}^{3}\). What volume in milliliters will \(20.0 \mathrm{~g}\) of gold occupy? (Hint: Don't be fooled. Remember that \(1 \mathrm{~cm}^{3}=1 \mathrm{~mL}\).)

Short Answer

Expert verified
The volume of 20.0 g of gold is approximately 1.0363 mL.

Step by step solution

01

Calculate the mass of gold in grams

We are given that the mass of gold is 20.0 g.
02

Use the density formula to find the volume

Density = mass/volume. In our case, we can rearrange the formula to solve for the volume: Volume = mass/density. We are given that the density of gold is 19.3 g/cm³. Calculate the volume using the given mass and density of gold: Volume (in cm³) = \( \frac{20.0 \mathrm{~g}}{19.3 \mathrm{~g}/\mathrm{cm}^{3}} \)
03

Simplify the expression and calculate the volume

Replace the given values in the expression and simplify: Volume (in cm³) = \( \frac{20.0 \mathrm{~g}}{19.3 \mathrm{~g}/\mathrm{cm}^{3}} \) = \( \frac{20.0 \mathrm{~g}}{1} \times \frac{1 \mathrm{cm}^{3}}{19.3 \mathrm{~g}} \) Volume (in cm³) = \( \frac{20.0}{19.3} \) cm³ = 1.0363 cm³
04

Convert the volume from cm³ to mL

We are given the conversion factor: 1 cm³ = 1 mL. Volume (in mL) = Volume (in cm³) = 1.0363 mL
05

State the final answer

The volume of 20.0 g of gold is approximately 1.0363 mL.

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