An intravenous saline drip has 9.0 g of sodium chloride per liter of water. By definition, 1 mL = 1 cm³. Express the salt concentration in kg/m³.

Verified step by step guidance

1. Step 1: Start by converting the given mass of sodium chloride from grams to kilograms. Since 1 kg = 1000 g, divide the given mass (9.0 g) by 1000 to express it in kilograms.
2. Step 2: Recognize that the volume of the solution is given as 1 liter, and by definition, 1 liter = 1000 mL = 1000 cm³ = 0.001 m³. Convert the volume to cubic meters (m³).
3. Step 3: Use the formula for concentration, which is defined as mass per unit volume: \( \text{Concentration} = \frac{\text{Mass}}{\text{Volume}} \). Substitute the mass in kilograms and the volume in cubic meters into this formula.
4. Step 4: Perform the division to calculate the concentration in \( \text{kg/m}^3 \). Ensure the units are consistent throughout the calculation.
5. Step 5: Verify the units of the final result to confirm that the concentration is expressed in \( \text{kg/m}^3 \), which is the desired unit for this problem.

Key Concepts

Concentration

Concentration refers to the amount of a substance (solute) present in a given volume of solution. It is commonly expressed in various units, such as grams per liter (g/L) or kilograms per cubic meter (kg/m³). Understanding concentration is essential for determining how much solute is dissolved in a solvent, which is crucial in fields like chemistry and medicine.

Unit Conversion

Unit conversion is the process of converting a quantity expressed in one set of units to another. In this context, converting grams per liter to kilograms per cubic meter involves recognizing that 1 g = 0.001 kg and 1 L = 0.001 m³. Mastery of unit conversion is vital for accurately interpreting and communicating scientific measurements.

Density of Water

The density of water is typically taken as 1 kg/L, which means that 1 liter of water has a mass of 1 kilogram. This property is important when calculating concentrations, as it allows for straightforward conversions between volume and mass. In the context of saline solutions, knowing the density helps in understanding how solutes interact with solvents.