Question

The density of platinum (Pt) is \(21.5 \mathrm{~g} / \mathrm{cm}^{3}\) at \(25^{\circ} \mathrm{C}\). What is the volume of \(87.6 \mathrm{~g}\) of \(\mathrm{Pt}\) at this temperature?

Short answer

The volume of 87.6 g of Pt is 4.08 cm³.

Step-by-step solution

Understand Density Formula

Density can be understood using the formula \( \text{Density} = \frac{\text{Mass}}{\text{Volume}} \). Rearranging this formula to find the volume gives \( \text{Volume} = \frac{\text{Mass}}{\text{Density}} \).

Identify Given Values

The problem states that the density of platinum is \(21.5 \, \text{g/cm}^3\) and the mass of the platinum sample is \(87.6 \, \text{g}\).

Plug Values into Formula

Using the formula for volume, \( \text{Volume} = \frac{\text{Mass}}{\text{Density}} \), substitute the given values: \( \text{Volume} = \frac{87.6}{21.5} \).

Calculate the Volume

Perform the division to find the volume: \( \text{Volume} = 4.072 \, \text{cm}^3 \).

Round Appropriately

Since the given data had three significant figures, the final answer should also be expressed in three significant figures: \(4.08 \, \text{cm}^3\).

Key concepts

Mass

Mass is a fundamental property that signifies the amount of matter in an object. It is typically measured in grams (g) or kilograms (kg). Mass is crucial in many scientific calculations, especially when determining the density of a material.
In the exercise, the mass of platinum (Pt) is given as 87.6 g. This value is essential for calculating the volume when the density is known.
It is important to note that mass is not affected by gravity, unlike weight, which can change depending on the planet's gravitational force.

Volume

Volume represents the amount of space that a substance or object occupies. Common units for measuring volume include cubic centimeters (cm³) and liters (L). In density calculations, understanding volume helps in determining how much space a certain mass of a substance will take up.
When given the mass and density, we can find the volume using the rearranged density formula: \[\text{Volume} = \frac{\text{Mass}}{\text{Density}} \] This is why in the problem, we substituted the mass (87.6 g) and the density (21.5 g/cm³) to find that the volume of platinum is approximately 4.08 cm³.

Significant Figures

Significant figures are crucial in scientific calculations as they indicate the precision of measured values. When performing calculations, the number of significant figures reflects the accuracy of the measurement.
Here's how to determine significant figures:

• All non-zero numbers are significant.
• Any zeros between significant digits are also significant.
• Leading zeros are not significant.
• Trailing zeros in a decimal number are significant.

In our platinum example, the mass was given as 87.6 g, which has three significant figures. To maintain precision, our calculated volume of 4.072 cm³ should be rounded to three significant figures, resulting in 4.08 cm³.

Density Formula

The density formula is a critical concept in understanding how mass and volume relate. The formula is defined as: \[\text{Density} = \frac{\text{Mass}}{\text{Volume}} \]Using this formula, we can determine either mass, volume, or density if the other two variables are known. In practical applications, this formula helps us understand the concentration of mass within a given volume.
For the given problem, the formula gets rearranged to find the volume: \[\text{Volume} = \frac{\text{Mass}}{\text{Density}} \] By knowing the density, 21.5 g/cm³, and the mass, 87.6 g, we utilized this formula to efficiently calculate that the volume of platinum is 4.08 cm³. It's a straightforward yet powerful tool in numerous fields of science and engineering.