Question

If \(1.5 \mathrm{g}\) of \(\mathrm{NaCl}\) is dissolved in enough water to make 1.0 L of solution, what is the molarity of \(\mathrm{NaCl}\) in the solution?

Short answer

The molarity of the NaCl solution is \(0.0257 M\), indicating there are \(0.0257\) moles of NaCl in every liter of the solution.

Step-by-step solution

Calculate the number of moles of NaCl

As stated in the problem, we know that we have 1.5 g of NaCl. To convert this mass to moles, we'll use the molar mass of NaCl, which is approximately 58.44 g/mol. Using the formula Moles = Mass / Molar mass, we obtain: Moles of NaCl = \(\frac{1.5 g}{58.44 g/mol} = 0.0257 mol\) So, there are 0.0257 moles of NaCl in the solution.

Calculate the molarity of the solution

Molarity is a measure of the concentration of a solute in a solution, or of any chemical species, in terms of amount of substance in a specified volume of solution. In this case, we want to find out the concentration of NaCl in the water. The volume of the solution is 1 liter. We use the formula Molarity (M) = Moles of solute / Volume of solution in liters Substituting in the values we have, we get Molarity = \(\frac{0.0257 mol}{1 L} = 0.0257 M\) Therefore, the molarity of the NaCl solution is 0.0257 M. This means there are 0.0257 moles of NaCl in every liter of the solution.

Key concepts

Molecular Weight

Molecular weight is a fundamental concept in chemistry, representing the mass of a single molecule of a particular substance.

• Every compound consists of atoms, and each atom has its own atomic weight.
• When you combine these atoms in various proportions, the total weight of all atoms involved gives the molecular weight.

For instance, in sodium chloride (NaCl), to find its molecular weight, you add the atomic weights of sodium (Na) and chlorine (Cl).
Sodium has an approximate atomic weight of 22.99, while chlorine has 35.45.
Adding these, the molecular weight of NaCl becomes 58.44 g/mol. Molecular weight is crucial when converting between grams and moles.
To find out how many moles are present in a given mass of a compound, we divide the mass by the molecular weight. Knowing the molecular weight allows chemists to make accurate calculations and predict the outcomes of chemical reactions.

Solute

A solute is a substance that is dissolved in a solvent to create a solution.

• In most cases, the solute is the substance present in a smaller amount.
• It can be a solid, liquid, or gas, depending on the solution being made.

Consider the classic example where table salt (NaCl) is dissolved in water.
Here, NaCl is the solute, while water is the solvent. The role of a solute in a solution is significant, as it determines the solution's chemical properties.
When a solute dissolves, its particles spread throughout the solvent, forming a uniform mixture. Different solutes have different solubility levels, meaning some dissolve better than others in specific solvents.
Understanding solutes helps us comprehend various solution behaviors, such as precipitation and concentration changes.

Solution Concentration

Solution concentration indicates how much solute is present in a given amount of solvent or solution. One of the most common ways to express concentration is through molarity, which measures the moles of solute per liter of solution.In the given exercise, the molarity of NaCl was calculated as 0.0257 M, meaning there are 0.0257 moles of NaCl in every liter of the solution.

Molarity is expressed in the units of moles per liter (mol/L). The formula for molarity is:

\[ \text{Molarity (M)} = \frac{\text{Moles of solute}}{\text{Volume of solution in liters}} \]Comprehending molarity helps us understand reaction rates, determine solution compositions, and predict the outcomes of reactions.
It is vital in laboratory settings and industrial applications where precise solution preparations are essential.Other units for expressing solution concentration include mass percent, ppm (parts per million), and molality, each useful in different scenarios.
This diverse range of units helps chemists to effectively formulate and alter solutions as needed.