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When you hear the word 'molarity,' it refers to the concentration of a solution. Specifically, it measures the number of moles of solute per liter of solution. In this context, we need to calculate the molarity of glucose in sparkling cider.

First, identify the amount of glucose provided, which is 22.0 grams. To find how many moles are present, we use the molecular weight. Glucose has the formula \(C_{6}H_{12}O_{6}\), and its molar mass is calculated as follows:

\[ (6 \times 12.01) + (12 \times 1.01) + (6 \times 16.00) = 180.16 \; \text{g/mol} \]

Thus, to determine the moles, we divide the grams of glucose by its molar mass:
\[ \text{Moles of glucose} = \frac{22.0 \; \text{g}}{180.16 \; \text{g/mol}} = 0.122 \; \text{mol} \]

Then, convert the volume of the cider from milliliters to liters. Here, 240 mL is equivalent to 0.240 L. Finally, apply the formula for molarity:

\[ M = \frac{\text{moles of solute}}{\text{liters of solution}} = \frac{0.122 \; \text{mol}}{0.240 \; \text{L}} = 0.508 \; \text{M} \]

This process allows you to understand the concentration of glucose in each serving, representing how densely glucose is packed into the cider.

The concentration of ions, like potassium, in a solution is also expressed in terms of molarity. Let's explore how to compute this for potassium ions in the cider.

Begin with the mass of potassium ions provided: 190 mg, which needs conversion to grams:

\[ 190 \; \text{mg} = 0.190 \; \text{g} \]

The molar mass of potassium ions \(\mathrm{K}^{+}\) is 39.10 g/mol. This allows us to determine the moles of \(\mathrm{K}^{+}\) as follows:

\[ \text{Moles of } \mathrm{K}^{+} = \frac{0.190 \; \text{g}}{39.10 \; \text{g/mol}} = 0.00486 \; \text{mol} \]

Given the volume of cider is 0.240 L, calculate the molarity:

\[ M = \frac{0.00486 \; \text{mol}}{0.240 \; \text{L}} = 0.02025 \; \text{M} \]

This indicates there is 0.02025 moles of \(\mathrm{K}^{+}\) per liter of cider, providing a clear understanding of how potassium ions are distributed in the beverage.

Sodium ion concentration, like that of glucose and potassium, also follows the same principles of molarity. To find this concentration, start by identifying the amount of sodium ions: 4.00 mg.

Convert milligrams to grams:
\[ 4.00 \; \text{mg} = 0.00400 \; \text{g} \]

Next, use the molar mass of sodium ions \(\mathrm{Na}^{+}\), which is 23.00 g/mol. Thus, you can calculate the moles of sodium ions by:

\[ \text{Moles of } \mathrm{Na}^{+} = \frac{0.00400 \; \text{g}}{23.00 \; \text{g/mol}} = 0.000174 \; \text{mol} \]

With the cider's volume in liters also set to 0.240, find the molarity of sodium ions:

\[ M = \frac{0.000174 \; \text{mol}}{0.240 \; \text{L}} = 0.000725 \; \text{M} \]

Through this calculation, you determine that there is a small concentration of sodium ions in the cider, illustrating its presence on a molar scale.