Copper has a density of 8.96 g/cm3. what is the mass of a sample of copper with a volume of 33.252 mL
The Correct Answer and Explanation is:
To find the mass of a copper sample, you use the formula:Mass=Density×Volume\text{Mass} = \text{Density} \times \text{Volume}Mass=Density×Volume
Given:
- Density of copper = 8.96 g/cm³
- Volume = 33.252 mL
Since 1 mL is equal to 1 cm³, the volume in cm³ is also 33.252 cm³.
Now plug the values into the formula:Mass=8.96 g/cm3×33.252 cm3\text{Mass} = 8.96 \, \text{g/cm}^3 \times 33.252 \, \text{cm}^3Mass=8.96g/cm3×33.252cm3Mass=297.94752 g\text{Mass} = 297.94752 \, \text{g}Mass=297.94752g
Final Answer:297.95 g(rounded to two decimal places)\boxed{297.95 \, \text{g}} \quad (\text{rounded to two decimal places})297.95g(rounded to two decimal places)
Explanation
To calculate the mass of a substance when its density and volume are known, you use the fundamental formula derived from the definition of density. Density is defined as the amount of mass per unit volume. Rearranging the formula for density gives you the mass. Specifically, multiplying the density by the volume gives the mass directly.
In this problem, the material is copper, and it has a density of 8.96 grams per cubic centimeter. The volume of the copper sample is given in milliliters. Since milliliters and cubic centimeters are equivalent in volume measurement (1 mL = 1 cm³), there is no need for any conversion between units in this case.
The volume provided is 33.252 mL, which means the same as 33.252 cm³. When you multiply this by the density, the cubic centimeters cancel out, and you are left with grams as the unit for mass. This operation gives a result of approximately 297.94752 grams. To make this value more readable and practical, it is rounded to two decimal places, giving a final answer of 297.95 grams.
This calculation shows how important it is to understand unit relationships and to apply simple multiplication in solving real-world chemistry and physics problems. Knowing how to manipulate formulas for physical properties like density allows you to find unknown values such as mass or volume, which are essential in laboratory and industrial settings.
