Calculate the number of moles of solute present in each of the following aqueous solutions: (b) 86.4 g of 0.180 m KCl,

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Identify the given information: mass of solvent (water) is 86.4 g and molality (m) is 0.180 m.

Convert the mass of the solvent from grams to kilograms, since molality is defined as moles of solute per kilogram of solvent.

Use the definition of molality: \( m = \frac{\text{moles of solute}}{\text{kilograms of solvent}} \) to set up the equation for moles of solute.

Rearrange the equation to solve for moles of solute: \( \text{moles of solute} = m \times \text{kilograms of solvent} \).

Substitute the known values into the equation to calculate the moles of solute.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Molarity (M)

Molarity is a measure of concentration defined as the number of moles of solute per liter of solution. It is expressed in units of moles per liter (mol/L). Understanding molarity is essential for calculating the amount of solute in a given volume of solution, which is crucial for solving the problem presented.

Moles of Solute

A mole is a unit in chemistry that represents 6.022 x 10²³ particles (atoms, molecules, etc.). To find the number of moles of solute in a solution, one can use the formula: moles = molarity × volume. This concept is vital for determining how much solute is present in the solution based on its concentration and volume.

Mass and Molar Mass

The mass of a substance is the amount of matter it contains, typically measured in grams. Molar mass is the mass of one mole of a substance, expressed in grams per mole (g/mol). To calculate the number of moles from a given mass, the formula used is: moles = mass (g) / molar mass (g/mol). This relationship is key to solving the problem regarding the amount of KCl in the solution.

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