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. To find the molarity of a solution, use the formula: Molarity (M) = moles of solute / liters of solution. For part (a), divide 0.5 moles of glucose by 1 liter of water.
2. For part (b), calculate the weight/volume percent concentration using the formula: (mass of solute in grams / volume of solution in mL) * 100. Convert 1 liter of water to 1000 mL and use 20 grams of sodium chloride.
3. For part (c), convert the concentration from grams per 100 mL to mg/dL. Since 1 gram = 1000 mg, multiply 1 gram by 1000 to get mg, then divide by 100 mL and multiply by 10 to convert to dL.
4. To find the molarity in part (d), use the formula: Molarity (M) = moles of solute / liters of solution. Convert 1 mmol to moles by dividing by 1000, then divide by 1 liter of water.
5. Ensure all units are consistent and correctly converted for each calculation to maintain accuracy in the final results.

Key Concepts

Molarity

Molarity is a measure of concentration defined as the number of moles of solute per liter of solution. It is expressed in moles per liter (mol/L) and is crucial for understanding how solutes interact in a solution. For example, a 0.5 M glucose solution contains 0.5 moles of glucose in one liter of water, which helps in calculating reactions and dilutions in microbiology.

Weight/Volume Percent

Weight/volume percent (w/v%) is a way to express the concentration of a solution, calculated as the mass of solute in grams per 100 mL of solution. For instance, a solution with 20 grams of sodium chloride in 1 liter of water would have a concentration of 2% w/v, which is important for preparing solutions in laboratory settings and understanding osmotic effects in microbial cells.

Concentration in mg/dL

Concentration in milligrams per deciliter (mg/dL) is commonly used in clinical and laboratory settings to express the amount of a substance in a specific volume of solution. For example, 1 gram of lactic acid in 100 mL translates to 1000 mg in 100 mL, or 1000 mg/dL. This unit is particularly relevant in microbiology for assessing metabolic products and their effects on microbial growth.