Question

A \(35.0-\mathrm{mL}\) sample of ethyl alcohol (density \(0.789 \mathrm{~g} / \mathrm{mL}\) ) is added to a graduated cylinder that has a mass of \(49.28 \mathrm{~g}\). What will be the mass of the cylinder plus the alcohol?

Short answer

The mass of the cylinder plus the alcohol is 76.895 g.

Step-by-step solution

Calculate the mass of the ethyl alcohol

Use the formula for mass, which is given by the product of density and volume. \[ \text{mass} = \text{density} \times \text{volume} \] The density (\rho) of ethyl alcohol is 0.789 g/mL and the volume (V) is 35.0 mL. \[ \text{mass} = 0.789 \frac{g}{mL} \times 35.0 \text{ mL} \] \[ \text{mass} = 27.615 \text{ g} \]

Determine the mass of the cylinder plus the alcohol

The mass of the cylinder is given as 49.28 g. To find the total mass, add the mass of the ethyl alcohol to the mass of the cylinder. \[ \text{Total mass} = \text{mass of cylinder} + \text{mass of alcohol} \] \[ \text{Total mass} = 49.28 \text{ g} + 27.615 \text{ g} \] \[ \text{Total mass} = 76.895 \text{ g} \]

Key concepts

Density

Density is a measure of how much mass is contained in a given unit volume of a substance. It is a physical property that can help identify materials and find their applications. The formula for density is \[ \text{density} = \frac{\text{mass}}{\text{volume}} \text{, which can be rearranged to find mass or volume if two of the three variables are known. } \]

In the exercise, the density of ethyl alcohol is provided as 0.789 g/mL. This means every milliliter of ethyl alcohol has a mass of 0.789 grams. By knowing the density and volume, you can easily calculate the mass.

Mass

Mass represents the amount of matter in an object, often measured in grams or kilograms. It is a fundamental property that does not change regardless of location, even in space.

To calculate the mass in the exercise, apply the formula \[ \text{mass} = \text{density} \times \text{volume}. \]

With a given density of 0.789 g/mL and a volume of 35.0 mL, the mass calculation goes as follows:
\[ \text{mass} = 0.789 \frac{g}{mL} \times 35.0 \text{ mL} = 27.615 \text{ g} \]

Therefore, the mass of the ethyl alcohol is 27.615 grams.

Volume

Volume measures the amount of space that a substance occupies, typically in liters (L) or milliliters (mL). It is a three-dimensional measure often used in conjunction with mass and density in various calculations.

In the exercise, the volume of ethyl alcohol is given as 35.0 mL. Volume helps determine the mass when combined with density. The relationship is straightforward when using the formula:
\[ \text{mass} = \text{density} \times \text{volume} \]

Knowing the volume is crucial in such problems, as it allows you to apply the density to find the total mass of the substance.

Graduated Cylinder

A graduated cylinder is a common laboratory instrument used to measure the volume of liquids accurately. It is typically marked with a scale to measure the liquid in milliliters or liters. When you add a substance to a graduated cylinder, the combined mass can be determined by the contents and the cylinder itself.

In the exercise, a graduated cylinder with a mass of 49.28 g is used. After calculating the mass of ethyl alcohol, you simply add this to the mass of the cylinder: \[ \text{Total mass} = 49.28 \text{ g} + 27.615 \text{ g} = 76.895 \text{ g} \]

This means the cylinder plus the ethyl alcohol will have a total mass of 76.895 grams, showcasing how graduated cylinders can help with such precise measurements.