Question

Using concentration as a conversion factor, how many moles of solute are in \(844 \mathrm{~mL}\) of \(2.09 \mathrm{M}\) \(\mathrm{MgSO}_{4} ?\)

Short answer

There are 1.76 moles of MgSO\(_4\) in 844 mL of 2.09 M solution.

Step-by-step solution

Understanding the Problem

We need to find the number of moles of solute (MgSO\(_4\)) in 844 mL of a 2.09 M MgSO\(_4\) solution. The molarity (M) is defined as moles of solute per liter of solution.

Convert Milliliters to Liters

Since molarity is expressed in terms of liters, convert the volume from milliliters to liters: \[ 844 \text{ mL} = 0.844 \text{ L} \]

Apply the Molarity Formula

Use the formula for molarity: \[ M = \frac{moles \ of \ solute}{liters \ of \ solution} \] Rearrange to find the moles of solute: \[ moles \ of \ solute = M \times liters \ of \ solution \]

Plug in the Values

Substitute the given values into the formula: \[ moles \ of \ solute = 2.09 \text{ M} \times 0.844 \text{ L} \]

Calculate the Moles of Solute

Perform the multiplication: \[ moles \ of \ solute = 2.09 \times 0.844 = 1.76436 \]

Round the Answer

Round the answer to an appropriate number of significant figures, based on the given data: \[ moles \ of \ solute = 1.76 \]

Key concepts

Concentration

When we talk about concentration, we are discussing how much of one substance is present in a given amount of another substance. In chemistry, concentration usually refers to the amount of solute (the substance being dissolved) in a solution. This is often expressed in terms of molarity.
Molarity (abbreviated as M) is a widely used unit of concentration in chemistry.
It represents the number of moles of solute dissolved in one liter of solution.

• Molarity = \( \frac{\text{moles of solute}}{\text{liters of solution}} \)
• This makes it easy to determine how concentrated a solution is, just by knowing the amount of solute and the volume of the solution.
• For example, a 1 M solution of magnesium sulfate (MgSO\(_4\)) contains 1 mole of MgSO\(_4\) in every liter of solution.

This is a key concept because concentration affects how solutions react in chemical processes. The more moles of solute present in the same amount of solvent, the more concentrated the solution, and often the more reactive it is.

Moles of Solute

The term "mole" is a fundamental concept in chemistry. It represents a specific quantity, \(6.022 \, \times \, 10^{23}\) of any chemical entity, whether it be atoms, molecules, ions, or other particles.

Understanding moles is important for quantifying how much solute is in your solution.

• To find the number of moles of a solute in a given solution, use the formula derived from molarity: \( \text{moles} = \text{M} \times \text{liters of solution} \).
• This formula allows you to easily calculate the actual amount of solute present just by knowing the molarity and the volume of the solution.
• In the original exercise, using this formula with the given values (2.09 M and 0.844 L), we determine that there are approximately 1.76 moles of MgSO\(_4\) present.

The concept of moles allows chemists to count particles by weighing them, which is invaluable for work in laboratory and industrial settings.

Conversion Factor

A conversion factor is a critical tool in chemistry and other sciences. It allows you to convert between different units of measurement.
In the context of molarity problems, conversion factors are often used to switch between milliliters and liters because molarity is defined in terms of liters.

• A common conversion in chemistry involves converting milliliters to liters, since there are 1000 milliliters in a liter.
• The conversion factor used to change milliliters to liters is: \(1 \, \text{L} = 1000 \, \text{mL}\).
• To convert 844 mL to liters, you multiply by the conversion factor: \( \frac{1 \, \text{L}}{1000 \, \text{mL}} \), which yields 0.844 L.

Understanding how to effectively use conversion factors ensures that calculations are accurate and that units are properly managed, which is crucial for producing correct, reliable results.