Chapter 4: Problem 113
A solution contains \(6.00 \%\) (by mass) \(\mathrm{NaBr}\) (sodium bromide). The density of the solution is \(1.046 \mathrm{~g} / \mathrm{cm}^{3} .\) What is the molarity of \(\mathrm{NaBr}\) ?
Short Answer
Expert verified
The molarity of \(\mathrm{NaBr}\) is \(0.610 \text{ M}\).
Step by step solution
01
Define Molarity
Molarity is defined as the number of moles of solute per liter of solution. Mathematically, it can be expressed as: \[ M = \frac{n}{V} \]where \( n \) is the moles of solute and \( V \) is the volume of the solution in liters.
02
Determine Mass of Solution
Assume we have 100 g of the solution for ease of calculation. This will contain \(6.00 \%\) of \(\mathrm{NaBr}\) by mass. Therefore, the mass of \(\mathrm{NaBr}\) in the solution is:\[ \text{Mass of NaBr} = 6.00 \text{ g} \]
03
Calculate Moles of NaBr
The molar mass of \(\mathrm{NaBr}\) is calculated by adding the atomic masses of \(\mathrm{Na}\) (23.00 g/mol) and \(\mathrm{Br}\) (79.90 g/mol), which is \(102.90\text{ g/mol}\). Then:\[ n = \frac{\text{Mass of NaBr}}{\text{Molar Mass of NaBr}} = \frac{6.00 \text{ g}}{102.90 \text{ g/mol}} = 0.0583 \text{ mol} \]
04
Calculate Volume of Solution
Using the density of the solution \(1.046 \text{ g/cm}^3\), calculate the volume of the 100 g solution:\[ \text{Volume} = \frac{\text{Mass}}{\text{Density}} = \frac{100 \text{ g}}{1.046 \text{ g/cm}^3} = 95.60 \text{ cm}^3 \] Convert this volume into liters: \[ V = 95.60 \text{ cm}^3 \times \frac{1 \text{ L}}{1000 \text{ cm}^3} = 0.0956 \text{ L} \]
05
Calculate Molarity of NaBr
Substitute the moles of \(\mathrm{NaBr}\) and the volume of the solution into the molarity formula:\[ M = \frac{0.0583 \text{ mol}}{0.0956 \text{ L}} = 0.610 \text{ M} \]Thus, the molarity of \(\mathrm{NaBr}\) in the solution is \(0.610 M\).
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Molarity
Molarity is a key concept in solution chemistry that helps us understand the concentration of a solution. It is defined as the number of moles of solute per liter of solution.
In simpler terms, it tells us how much of a substance is present in a certain amount of solution.
In simpler terms, it tells us how much of a substance is present in a certain amount of solution.
- Formula: \( M = \frac{n}{V} \) where \( M \) is the molarity, \( n \) is the moles of solute, and \( V \) is the volume of solution in liters.
- Molarity is often represented as M.
Mass Percent
Mass percent, sometimes referred to as percent by weight, is a way of expressing the concentration of a component in a mixture. It indicates how much of a specific substance is present compared to the total mass of the mixture.
- It is expressed as: \( \text{Mass Percent} = \left( \frac{\text{Mass of solute}}{\text{Total mass of solution}}\right) \times 100 \% \).
- This value is generally more intuitive and easier to work with for small-scale lab settings.
Density
Density is another crucial concept, especially in solution chemistry, as it connects the mass of a substance with its volume. It is defined as the mass per unit volume of a substance.
- The formula is: \( \text{Density} = \frac{\text{Mass}}{\text{Volume}} \).
- In our exercise, the density is given as \(1.046 \text{ g/cm}^3\), meaning each cubic centimeter of the solution weighs 1.046 grams.
Moles Calculation
Understanding moles calculation is fundamental in chemistry to convert between the mass of a substance and its quantity in moles. Moles give a count of the number of molecules or atoms present, based on the particles' average mass compared to carbon-12.
- The formula used is: \( n = \frac{\text{Mass}}{\text{Molar Mass}} \), where \( n \) is the number of moles.
- The molar mass of NaBr is calculated as: \(102.90 \text{ g/mol}\), combining the atomic mass of Na and Br.