Determine the following:
a. The molarity of a solution with 0.5 moles of glucose per liter of water.
b. The concentration (in weight/volume percent) of a solution that contains 20 grams of sodium chloride per liter of water.
c. The concentration (in mg/dL) of a solution with 1 gram of lactic acid per 100 mL of solution.
d. The molarity of a solution with 1 mmol of solute in 1 L of water.

Verified step by step guidance

1. For part (a), recall that molarity (M) is defined as the number of moles of solute divided by the volume of the solution in liters. Use the formula: \(M = \frac{\text{moles of solute}}{\text{volume of solution in liters}}\). Here, you have 0.5 moles of glucose per liter, so substitute these values into the formula.
2. For part (b), weight/volume percent (% w/v) is calculated as the mass of solute in grams divided by the volume of solution in milliliters, multiplied by 100. Use the formula: \(\% \text{w/v} = \left( \frac{\text{grams of solute}}{\text{mL of solution}} \right) \times 100\). Convert 1 liter to milliliters (1000 mL) and substitute the given values.
3. For part (c), concentration in mg/dL means milligrams of solute per deciliter of solution. First, convert 1 gram of lactic acid to milligrams (1 g = 1000 mg). Then, note that 100 mL equals 1 deciliter (dL). Use the formula: \(\text{mg/dL} = \frac{\text{mg of solute}}{\text{dL of solution}}\) and substitute the values.
4. For part (d), molarity is again moles of solute per liter of solution. Here, 1 mmol (millimole) is equal to 0.001 moles. Use the formula: \(M = \frac{\text{moles of solute}}{\text{volume in liters}}\). Since the volume is 1 L, substitute the values accordingly.
5. After setting up each formula with the correct units and values, perform the arithmetic operations to find the numerical concentrations for each part.

Key Concepts

Molarity

Molarity is a measure of the concentration of a solute in a solution, expressed as moles of solute per liter of solution. It is commonly used in chemistry to quantify how much of a substance is dissolved in a given volume, facilitating stoichiometric calculations in reactions.

Weight/Volume Percent Concentration

Weight/volume percent (% w/v) expresses the concentration of a solution as grams of solute per 100 milliliters of solution. It is useful for describing solutions where the solute is a solid dissolved in a liquid, providing a straightforward way to communicate concentration in practical lab settings.

Unit Conversions in Concentration Measurements

Understanding unit conversions, such as milligrams per deciliter (mg/dL) or millimoles to moles, is essential for accurately interpreting and calculating solution concentrations. These conversions allow comparison and communication of concentrations across different measurement systems.