Q.2.78 - An Introduction to General, Organic, and Biological Chemistry

Question

Solve each of the following problems: 

a. A glucose solution has a density of 1.02 g/mL. What is its specific gravity? 

b. A 0.200 mL sample of very-low-density lipoprotein (VLDL) has a mass of 190 mg. What is the density of the VLDL? 

c. Butter has a specific gravity of 0.86. What is the mass, in grams, of 2.15 L of butter? 

d. A 5.000-mL urine sample has a mass of 5.025 g. If the normal range for the specific gravity of urine is 1.003 to 1.030, would the specific gravity of this urine sample indicate that the patient could have type 2 diabetes? 

Step-by-Step Solution

Answer

a.  The specific gravity of glucose solution is 1.02. 

b. The density of VLDL is 0.95 g/mL. 

c. The mass of butter is 1849 g. 

d. No, the person is not suffering from diabetes 2.

Step 1: part (a) Given Information

The density of the glucose solution is 1.02 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.

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

On substituting the given values in the above formula: 

$$\begin{gathered} \mathrm{Specific} \mathrm{gravity}=\frac{1.02 \mathrm{g}/\mathrm{mL}}{1.00 \mathrm{g}/\mathrm{mL}} \\ \mathrm{Specific} \mathrm{gravity}=1.02 \end{gathered}$$

Thus, the specific gravity of glucose solution is 1.02.

Step 1: Part (b) Given Information

The volume of the sample is 20.0 mL

The mass of the sample is 190 mg.

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:

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

Unit conversion for mg into g:

$$\begin{gathered} 1 \mathrm{mg}=0.001 \mathrm{g} \\ \mathrm{So}, \\ 190 \mathrm{mg}=190\times 0.001 =0.19 \mathrm{g} \end{gathered}$$

On substituting the given formula in the above formula: 

$$\begin{gathered} \mathrm{Density}=\frac{0.19 \mathrm{g}}{0.200 \mathrm{mL}} \\ \mathrm{Density}=0.95 \mathrm{g}/\mathrm{mL} \end{gathered}$$

Thus, the density of VLDL is 0.95 g/mL.

Step 1: Part (c) Given Information

The specific gravity of butter=0.86.

Volume=2.15 L or 2150 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:

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

On rearranging and substituting the given values: 

$$\begin{gathered} \mathrm{Density} \mathrm{of} \mathrm{substance}= \mathrm{Specific} \mathrm{gravity}\times \mathrm{Density} \mathrm{of} \mathrm{water} \\ \mathrm{Density} \mathrm{of} \mathrm{substance}=0.86\times 1.00 \mathrm{g}/\mathrm{mL} \\ \mathrm{Density} \mathrm{of} \mathrm{substance}=0.86 \mathrm{g}/\mathrm{mL} \end{gathered}$$

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: 

$$\begin{gathered} \mathrm{Mass} \mathrm{of} \mathrm{butter}= \mathrm{Density} \times \mathrm{Volume} \\ \mathrm{Mass} \mathrm{of} \mathrm{butter}=0.86 \mathrm{g}/\mathrm{mL}\times 2150 \mathrm{mL} \\ \mathrm{Mass} \mathrm{of} \mathrm{butter}=1849 \mathrm{g} \end{gathered}$$

Thus, the mass of butter is 1849 g.

Step 1: Part (d) Given Information

Volume of urine sample=5.000 mL

Mass= 5.025 g

Step 2: Part (d) 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 values:

$$\begin{gathered} \mathrm{Density}=\frac{5.025 \mathrm{g}}{5.000 \mathrm{mL}} \\ \mathrm{Density}=1.005 \mathrm{g}/\mathrm{mL} \end{gathered}$$

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:

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

On substituting the values:

$$\begin{gathered} \mathrm{Specific} \mathrm{gravity}=\frac{1.005 \mathrm{g}/\mathrm{mL}}{1 \mathrm{g}/\mathrm{mL}} \\ \mathrm{Specific} \mathrm{gravity}=1.005 \end{gathered}$$

The normal range of specific gravity for a urine sample is 1.003 to 1.030. Thus we can conclude that the person is not suffering from diabetes 2.