In a sugar tolerance test, a patient needs to drink a glucose (C6H12O6) solution containing 100g glucose. Given that one cup is 350 mL, calculate the molarity of glucose in the glucose solution.

Verified step by step guidance

1. Step 1: Calculate the number of moles of glucose. Use the molar mass of glucose (C_6H_{12}O_6), which is approximately 180.18 g/mol, to convert 100 g of glucose to moles using the formula: \( \text{moles of glucose} = \frac{\text{mass of glucose (g)}}{\text{molar mass of glucose (g/mol)}} \).
2. Step 2: Convert the volume of the solution from milliliters to liters. Since 1 cup is 350 mL, convert this volume to liters by using the conversion factor: \( 1 \text{ L} = 1000 \text{ mL} \).
3. Step 3: Calculate the molarity of the glucose solution. Molarity (M) is defined as the number of moles of solute (glucose) per liter of solution. Use the formula: \( M = \frac{\text{moles of solute}}{\text{liters of solution}} \).
4. Step 4: Substitute the values obtained from Steps 1 and 2 into the molarity formula to find the molarity of the glucose solution.
5. Step 5: Review the units to ensure they are consistent and correct, confirming that the final unit for molarity is moles per liter (mol/L).

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). To calculate molarity, one must know the amount of solute in grams and the volume of the solution in liters. This concept is essential for understanding how concentrated a solution is and is commonly used in chemistry for preparing solutions.

Moles and Molar Mass

A mole is a unit in chemistry that represents 6.022 x 10²³ entities, such as atoms or molecules. The molar mass of a substance is the mass of one mole of that substance, typically expressed in grams per mole (g/mol). For glucose (C6H12O6), the molar mass is approximately 180 g/mol. Knowing how to convert grams of a substance to moles is crucial for calculating molarity.

Volume Conversion

Volume conversion is the process of changing a measurement from one unit to another, such as from milliliters (mL) to liters (L). Since molarity is defined in terms of liters, it is necessary to convert the volume of the solution from mL to L for accurate calculations. For example, 350 mL is equivalent to 0.350 L, which is essential for determining the molarity of the glucose solution.