Question

Glycerol has a density of \(1.20 \mathrm{~g} / \mathrm{mL}\). How many \(\mathrm{mL}\) are in \(75 \mathrm{~g}\) of glycerol?

Short answer

The volume is 62.5 mL.

Step-by-step solution

Identify the Given Values

The problem provides the density of glycerol as \(1.20 \mathrm{\frac{g}{mL}}\) and the mass of glycerol as \(75 \mathrm{g}\).

Recall the Density Formula

The formula for density is given by \[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]. We need to rearrange this formula to solve for volume.

Rearrange the Formula

To find the volume, rearrange the density formula to get \[ \text{Volume} = \frac{\text{Mass}}{\text{Density}} \].

Substitute the Given Values

Substitute the mass and density into the rearranged formula: \[ \text{Volume} = \frac{75 \ \mathrm{g}}{1.20 \ \mathrm{\frac{g}{mL}}} = \frac{75}{1.20} \].

Calculate the Volume

Divide \(75 \mathrm{g}\) by \(1.20 \mathrm{\frac{g}{mL}}\) to find the volume: \[ \frac{75}{1.20} = 62.5 \ \mathrm{mL} \].

Key concepts

Mass and Volume Relationship

Understanding the relationship between mass and volume is crucial in density calculations. Mass is the amount of matter in an object, typically measured in grams (g). Volume is the amount of space an object occupies, measured in milliliters (mL) for liquids. In density problems, knowing how these two quantities interact helps solve for the unknown. When we know the mass and density of a substance, we can find the volume, and vice versa. Remember: increasing the mass while keeping volume constant increases the density. Decreasing the volume while keeping mass constant does the same. This relationship is foundational to mastering density calculations.

Density Formula

The density formula is a simple yet powerful tool in physics and chemistry. It is given by \[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]. Here, density is the ratio of mass to volume. For instance, if we know the mass and density of a substance, we can rearrange the formula to solve for the volume: \[ \text{Volume} = \frac{\text{Mass}}{\text{Density}} \]. This rearrangement allows us to find any one of the three variables (mass, volume, density) if we have the other two. Substituting known values into the formula and solving will yield the desired result. The key is to keep the units consistent to avoid errors.

Unit Conversion

Unit conversion often plays a role in density calculations. The solution to the exercise used grams for mass and milliliters for volume. It’s important to ensure the units match those given in the problem. If the mass was provided in kilograms (kg) instead of grams, or if volume was in liters (L) instead of milliliters, conversion is necessary. For example: \[ 1 \ \text{kg} = 1000 \ \text{g} \] and \[ 1 \ \text{L} = 1000 \ \text{mL} \]. Converting appropriately ensures the calculation is accurate. Keep a conversion chart handy to quickly reference common conversions, aiding in accurate and easy calculations.