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Chapter 9: Problem 64

What is the concentration of a \(\mathrm{NaCl}\) solution, in \((\mathrm{m} / \mathrm{v}) \%,\) prepared by diluting \(65 \mathrm{~mL}\) of a saturated solution, which has a concentration of \(37(\mathrm{~m} / \mathrm{v}) \%\), to \(480 \mathrm{~mL}\) ?

Short Answer

Expert verified
The concentration is 5.01% (m/v).

Step by step solution

01

Understand the Problem

We have a saturated solution of NaCl with a concentration of 37% (m/v) in 65 mL. We want to know the concentration of this solution when it's diluted to 480 mL.
02

Calculate Amount of NaCl in Original Solution

Calculate the mass of NaCl in the original 65 mL. Since the concentration is given as 37% (m/v), this means there are 37 grams of NaCl in 100 mL of solution. Thus, the mass of NaCl in 65 mL is: \( \frac{37 ext{ g}}{100 ext{ mL}} \times 65 ext{ mL} = 24.05 ext{ g} \).
03

Determine Final Volume of Solution

The solution is diluted to a final total volume of 480 mL. This is the volume we will use to calculate the new concentration.
04

Calculate New Concentration in (m/v) %

Use the mass of NaCl and the final volume of the solution to calculate the new concentration: \( \text{New concentration} = \left( \frac{\text{Mass of NaCl}}{\text{Final Volume}} \right) \times 100\). The new concentration is: \( \frac{24.05 ext{ g}}{480 ext{ mL}} \times 100 = 5.01\% \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Solution Concentration
Solution concentration refers to the amount of a solute that is dissolved in a given quantity of solvent. A common way to express concentration is through mass/volume percent (m/v %). This indicates the grams of solute per 100 milliliters of solution. For example, a 37% (m/v) NaCl solution contains 37 grams of NaCl in every 100 milliliters of solution.
  • High concentration means more solute is dissolved.
  • Low concentration means less solute is present.
  • In dilution, concentration decreases as the volume of solvent increases.
Understanding concentration is crucial in determining how to dilute solutions or achieve a desired strength in solutions, which is essential in both laboratory and everyday applications.
Saturated Solution
A saturated solution is one in which the maximum amount of solute has been dissolved in the solvent at a given temperature. Beyond this point, no additional solute will dissolve unless temperature changes.
  • Equilibrium is reached when the rate of solute dissolving equals the rate of solute coming out of solution.
  • Saturated solutions are useful for understanding the solubility of a substance at specific conditions.
  • In our example, the NaCl solution was initially saturated at 37% (m/v), meaning it couldn't hold more solute at that temperature.
When diluting a saturated solution, you redistribute the solute throughout more solvent, which typically unsaturates the solution.
Mass/Volume Percent
Mass/volume percent (m/v) is a way to express concentration, calculated by dividing the mass of solute by the total volume of solution and then multiplying by 100 to convert to a percentage.Let's break down the formula:\[ \text{(m/v)}\% = \left( \frac{\text{mass of solute (g)}}{\text{volume of solution (mL)}} \right) \times 100 \]This allows easy comparison of solution strengths, independent of the actual weights or volumes. In practice:
  • Calculate the solute mass using the given concentration before dilution.
  • Use the new volume after dilution to find the new concentration.
  • In our example, after dilution to 480 mL, the concentration becomes 5.01% (m/v), demonstrating how to adjust concentrations by altering volumes and calculating accordingly.

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Most popular questions from this chapter

The solubility of \(\mathrm{CO}_{2}\) gas in water is \(0.15 \mathrm{~g} / 100 \mathrm{~mL}\) at a \(\mathrm{CO}_{2}\) pressure of \(101,325 \mathrm{~Pa}\). (a) What is the solubility of \(\mathrm{CO}_{2}\) in a soft drink (which is mainly water) that was bottled under a \(\mathrm{CO}_{2}\) pressure of \(4.6 \times 10^{5} \mathrm{~Pa} ?\) (b) An atmospheric concentration of \(380 \mathrm{ppm}, \mathrm{CO}_{2}\) corresponds to a partial pressure of \(38.5 \mathrm{~Pa}\). What percentage of the \(\mathrm{CO}_{2}\) originally dissolved in the solution in part (a) remains in solution after the soft drink reaches equilibrium with the ambient atmosphere? (c) One bottle of soda is stored in a refrigerator at \(3^{\circ} \mathrm{C}\) \((276 \mathrm{~K})\), and another is stored at room temperature \(\left(25^{\circ} \mathrm{C}\right.\) or \(\left.298 \mathrm{~K}\right)\). If both bottles are opened simultaneously, which one would exhibit greater carbonation (i.e., bubbles)? Explain.

Which of the following solutions will give rise to a greater osmotic pressure at equilibrium: \(5.00 \mathrm{~g}\) of \(\mathrm{NaCl}\) in \(350.0 \mathrm{~mL}\) water or \(35.0 \mathrm{~g}\) of glucose in \(400.0 \mathrm{~mL}\) water? For \(\mathrm{NaCl}\), molecular mass \(=58.5\) amu; for glucose, molecular mass \(=180\) amu.

Methanol, \(\mathrm{CH}_{3} \mathrm{OH}\), is sometimes used as an antifreeze for the water in automobile windshield washer fluids. How many moles of methanol must be added to \(5.00 \mathrm{~kg}\) of water to lower its freezing point to \(-10.0^{\circ} \mathrm{C}(263 \mathrm{~K}) ?\) (For each mole of solute, the freezing point of \(1 \mathrm{~kg}\) of water is lowered \(1.86^{\circ} \mathrm{C} / \mathrm{K} .\) )

An aqueous solution that contains 285 ppm of potassium nitrate \(\left(\mathrm{KNO}_{3}\right)\) is being used to feed plants in a garden. What volume of this solution is needed to prepare \(2.0 \mathrm{~L}\) of a solution that is \(75 \mathrm{ppm}\) in \(\mathrm{KNO}_{3}\) ?

Emergency treatment of cardiac arrest victims sometimes involves injection of a calcium chloride solution directly into the heart muscle. How many grams of \(\mathrm{CaCl}_{2}\) are administered in an injection of \(5.0 \mathrm{~mL}\) of a \(5.0 \%(\mathrm{~m} / \mathrm{v})\) solution? How many milliequivalents of \(\mathrm{Ca}^{2+}\) ?
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