Q.2.77 - An Introduction to General, Organic, and Biological Chemistry

Question

Solve each of the following problems: 

a. A urine sample has a density of 1.030 g/mL. What is the specific gravity of the sample? 

b. A 20.0-ml sample of a glucose IV solution has a mass of 20.6 g. What is the density of the glucose solution? 

c. The specific gravity of vegetable oil is 0.92. What is the mass, in grams, of 750 mL of vegetable oil? 

d. A bottle containing 325 g of cleaning solution is used to clean hospital equipment. If the cleaning solution has a specific gravity of 0.850, what volume, in milliliters, of solution was used?

Step-by-Step Solution

Answer

a. 1.03

b. 1.03 g/mL

c. 690 g

d. 382 mL

Step 1: Part (a) Given Information

A urine sample has a density of 1.030 g/mL.

Step 2: Part (a) Explanation

Specific gravity tells the relation between the density of a substance and the density of water. It can be calculated by dividing these two quantities.

The density of water is 1.00 g/mL at 4^oC.

Specific gravity can be given as:

$\mathrm{Specific} \mathrm{gravity}=\frac{\mathrm{density} \mathrm{of} \mathrm{substance}}{\mathrm{densit}y \mathrm{of} \mathrm{water}}$

On substituting the given values in the above formula:

$\mathrm{Specific} \mathrm{gravity} = \frac{1.030 \mathrm{g}/\mathrm{mL}}{1.00 \mathrm{g}/\mathrm{mL}}=1.03$

Thus, the specific gravity or urine sample is 1.03.

Step 1: Part (b) Given Information

Volume of glucose IV solution = 20.0 mL

Mass of sample= 20.6 g

Step 2: Part (b) Explanation

Density defines the relationship between the mass and volume of a substance. Every substance has its own unique density.

It is given as:

$\mathrm{Density}=\frac{\mathrm{mass} \mathrm{of} \mathrm{substance}}{\mathrm{volume} \mathrm{of} \mathrm{substance}}$

On substituting the given formula in the above formula:

$$\begin{gathered} \mathrm{Density}=\frac{20.6 \mathrm{g}}{20.0 \mathrm{mL}} \\ \mathrm{Density}=1.03 \mathrm{g}/\mathrm{mL} \end{gathered}$$

Thus, the density of the solution is 1.03 g/mL.

Step 1: Part (c) Given Information

The specific gravity of vegetable oil is 0.92. 

Volume of vegetable oil =750 mL

Step 2: Part (c) Explanation

Specific gravity tells the relation between the density of a substance and the density of water. It can be calculated by dividing these two quantities.

The density of water is 1.00 g/mL at 4^oC.

Specific gravity can be given as:

$\mathrm{Specific} \mathrm{gravity}=\frac{\mathrm{density} \mathrm{of} \mathrm{substance}}{\mathrm{densit}y \mathrm{of} \mathrm{water}}$

On rearranging and substituting the given values:

$$\begin{gathered} \mathrm{Density} \mathrm{of} \mathrm{substance}= \mathrm{Specific} \mathrm{gravity} \times \mathrm{Density} \mathrm{of} \mathrm{water} \\ \mathrm{Density} \mathrm{of} \mathrm{substance}=0.92 \times 1.00 \mathrm{g}/\mathrm{mL} \\ \mathrm{Density} \mathrm{of} \mathrm{substance}= 0.92 \mathrm{g}/\mathrm{mL} \end{gathered}$$

The calculation for mass:

Density defines the relationship between the mass and volume of a substance. It is given as:

$\mathrm{Density}=\frac{\mathrm{mass} \mathrm{of} \mathrm{substance}}{\mathrm{volume} \mathrm{of} \mathrm{substance}}$

On rearranging and substituting the given values:

$$\begin{gathered} \mathrm{Mass} \mathrm{of} \mathrm{vegetable} \mathrm{oil}=\mathrm{Density}\times \mathrm{Volume} \\ \mathrm{Mass} \mathrm{of} \mathrm{vegetable} \mathrm{oil}=0.92 \mathrm{g}/\mathrm{mL}\times 750 \mathrm{mL} \\ \mathrm{Mass} \mathrm{of} \mathrm{vegetable} \mathrm{oil}=690 \mathrm{g} \end{gathered}$$

Thus, the mass of vegetable oil is 690 grams.

Step 1: Part (d) Given Information

Mass of cleaning solution = 325 g

The specific gravity of the cleaning solution = 0.850

Step 2: Part (d) Explanation

Specific gravity tells the relation between the density of a substance and the density of water. It can be calculated by dividing these two quantities.

The density of water is 1.00 g/mL at 4^oC.

It is given as:

$\mathrm{Specific} \mathrm{gravity}=\frac{\mathrm{density} \mathrm{of} \mathrm{substance}}{\mathrm{densit}y \mathrm{of} \mathrm{water}}$

On rearranging and substituting the given values:

$$\begin{gathered} \mathrm{Density} \mathrm{of} \mathrm{substance}= \mathrm{Specific} \mathrm{gravity} \times \mathrm{Density} \mathrm{of} \mathrm{water} \\ \mathrm{Density} \mathrm{of} \mathrm{substance}=0.850 \times 1.00 \mathrm{g}/\mathrm{mL} \\ \mathrm{Density} \mathrm{of} \mathrm{substance}= 0.850 \mathrm{g}/\mathrm{mL} \end{gathered}$$

The calculation for Volume:

Density defines the relationship between the mass and volume of a substance. It is given as:

$\mathrm{Density}=\frac{\mathrm{mass} \mathrm{of} \mathrm{substance}}{\mathrm{volume} \mathrm{of} \mathrm{substance}}$

On rearranging and substituting the given values:

$$\begin{gathered} \mathrm{Volume} \mathrm{of} \mathrm{cleaning} \mathrm{solution}= \frac{\mathrm{Mass}}{\mathrm{Density}} \\ \mathrm{Volume} \mathrm{of} \mathrm{cleaning} \mathrm{solution}= \frac{325 \mathrm{g}}{0.850 \mathrm{g}/\mathrm{mL}} \\ \mathrm{Volume} \mathrm{of} \mathrm{cleaning} \mathrm{solution}= 382.35 \mathrm{mL} \approx 382 \mathrm{mL} \end{gathered}$$

Thus, the volume of cleaning solution is 382 mL.