Question

The concentration of glucose \(\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right)\) in normal blood is approximately \(90 \mathrm{mg}\) per \(100 \mathrm{~mL}\). What is the molarity of the glucose?

Short answer

The molarity of glucose in normal blood is 0.005 M.

Step-by-step solution

Convert Mass to Grams

The glucose concentration is given as 90 mg per 100 mL. First, convert the mass of glucose into grams. Since 1 mg = 0.001 g, multiply 90 mg by 0.001 to get the mass in grams, which yields 0.09 g glucose.

Calculate Moles of Glucose

Use the molar mass of glucose (C_6H_{12}O_6), which is 180 g/mol, to calculate the number of moles in 0.09 g of glucose. Use the formula:\[ \text{Moles of glucose} = \frac{\text{mass in grams}}{\text{molar mass}} = \frac{0.09}{180} \approx 0.0005 \text{ moles} \].

Convert mL to Liters

Convert 100 mL of solution into liters since molarity is expressed in terms of liters. Recall that 1 L = 1000 mL, so 100 mL equals 0.1 L.

Calculate Molarity

Molarity is defined as the number of moles of solute per liter of solution. Use the formula: \[ \text{Molarity (M)} = \frac{\text{moles of solute}}{\text{liters of solution}} = \frac{0.0005}{0.1} = 0.005 \text{M} \].

Key concepts

Glucose Concentration

Glucose concentration in blood is crucial because it reflects our body's energy supply. Blood glucose concentration is often described in terms of milligrams (mg) per deciliter (dL) or per 100 milliliters (mL). In the exercise, the glucose concentration is given as 90 mg per 100 mL. This means there are 90 milligrams of glucose in every 100 mL of blood. This measure helps in assessing an individual's blood sugar levels which is vital for diagnosing conditions like diabetes. Understanding glucose concentration is the first step in calculating other important values like molarity.

Mole Conversion

Mole conversion is essential in chemistry for understanding quantities at the molecular level. A mole is a standard scientific unit that quantifies amounts of a chemical substance. In the exercise, you start by converting the mass of glucose from milligrams to grams. Since there are 1000 milligrams in a gram, you multiply by 0.001, converting 90 mg into 0.09 g.

Next, you need to convert this mass into moles using the molar mass of glucose (C_6H_{12}O_6), which is 180 g/mol. The formula for this conversion is: \(\text{Moles} = \frac{\text{mass in grams}}{\text{molar mass}}\), resulting in 0.0005 moles of glucose. This conversion reveals how many glucose molecules you're dealing with on a molecular level.

Solution Concentration

Solution concentration refers to how much solute (in this case, glucose) is present in a given volume of solution. Molarity is a common way to express concentration because it standardizes the measure, making it easy to communicate and understand chemical quantities. It's calculated by dividing the moles of solute by the liters of solution.

In our step-by-step exercise, you've converted 100 mL of blood to 0.1 liters (since 1 L = 1000 mL). Molarity is then calculated as: \[ \text{Molarity} (M) = \frac{\text{0.0005 moles}}{\text{0.1 L}} = 0.005 M \]. This calculation provides a clear, standardized concentration that can easily be used in further chemical analysis or comparison.

Molality vs Molarity

Molality and molarity both measure concentration but differ in application and calculation basis.

• Molarity is determined by the number of moles of solute per liter of solution. It's temperature-dependent since fluid volumes can expand or contract with temperature changes.
  
  
• Molality, on the other hand, focuses on the mass of the solvent. It's calculated as moles of solute per kilogram of solvent and is not affected by temperature changes.

Understanding the difference between these two is crucial in scenarios where temperature variation might affect volume, thus requiring a more stable measurement like molality. In solutions like blood, molarity is often preferred for ease and consistency despite its temperature sensitivity.