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?

Verified step by step guidance

1. Understand the concept of specific gravity: Specific gravity is a dimensionless quantity that compares the density of a substance to the density of water at a specific temperature (usually 4°C, where the density of water is approximately 1.000 g/mL). The formula for specific gravity is: $\mathrm{Specific}\mathrm{Gravity}=\frac{\mathrm{Density}\left(\mathrm{sample}\right)}{\mathrm{Density}\left(\mathrm{water}\right)}$.
2. Identify the given values: The density of the urine sample is provided as 1.030 g/mL, and the density of water is approximately 1.000 g/mL at 4°C.
3. Substitute the values into the formula: Replace the density of the sample and the density of water in the formula for specific gravity. This gives: $\mathrm{Specific}\mathrm{Gravity}=\frac{1.030 g/\mathrm{mL}}{1.000 g/\mathrm{mL}}$.
4. Perform the division: Divide the density of the urine sample (1.030 g/mL) by the density of water (1.000 g/mL). Since the units cancel out, the result will be a dimensionless number.
5. Interpret the result: The specific gravity of the urine sample is a comparison to water, and the value obtained indicates how much denser the urine sample is relative to water. Specific gravity values greater than 1 indicate the sample is denser than water.

Key Concepts

Density

Density is defined as the mass of a substance per unit volume, typically expressed in grams per milliliter (g/mL) or kilograms per cubic meter (kg/m³). It is a fundamental property that helps in identifying substances and understanding their behavior in different environments. In this context, the density of the urine sample is given as 1.030 g/mL, which is crucial for calculating its specific gravity.

Specific Gravity

Specific gravity is a dimensionless quantity that compares the density of a substance to the density of a reference substance, usually water at 4°C, which has a density of 1.000 g/mL. It is calculated by dividing the density of the substance by the density of water. Specific gravity provides insight into the concentration of solutes in a solution, making it particularly useful in medical diagnostics, such as evaluating urine samples.

Calculation of Specific Gravity

To calculate specific gravity, the formula used is: Specific Gravity = Density of the substance / Density of water. For the urine sample with a density of 1.030 g/mL, the specific gravity can be determined by dividing this value by the density of water (1.000 g/mL). This calculation allows for a straightforward comparison of the urine's density relative to water, indicating its concentration and potential health implications.