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Chapter 16: Problem 115

Sodium chloride is added to water (at \(25^{\circ} \mathrm{C}\) ) until it is saturated. Calculate the \(\mathrm{Cl}^{-}\) concentration in such a solution.

Short Answer

Expert verified
The concentration of \(\mathrm{Cl}^{-}\) ions in a saturated sodium chloride solution at \(25^{\circ} \mathrm{C}\) is approximately 6.01 mol/L.

Step by step solution

01

Write the dissolution equation for sodium chloride

Write the balanced equation for the dissolution process of sodium chloride: \(NaCl \rightleftharpoons Na^+ + Cl^-\)
02

Find the solubility product constant (Ksp) for sodium chloride at 25°C

The Ksp value for sodium chloride at 25°C is 36.1. This value can be found in reference tables or online.
03

Write the expression for the solubility product constant (Ksp)

Write the expression for Ksp based on the equation from Step 1: \(K_{sp} = [Na^+][Cl^-]\)
04

Determine the relationship between the concentrations of ions

Based on the stoichiometry of the dissolution equation, the concentration of Na⁺ and Cl⁻ ions will be equal at saturation. Let's use 'x' to represent the concentration of both ions at saturation: \([Na^+] = [Cl^-] = x\)
05

Substitute the values into the Ksp expression

Use the relationship from Step 4 to substitute the concentrations of Na⁺ and Cl⁻ in the Ksp expression from Step 3: \(K_{sp} = (x)(x) = x^2\)
06

Calculate the concentration of Cl⁻ ions at saturation

Substitute the Ksp value from Step 2 into the equation from Step 5 and solve for 'x': \(x^2 = 36.1\) \(x = \sqrt{36.1} \approx 6.01\) Thus, the concentration of Cl⁻ ions in the saturated sodium chloride solution at 25°C is approximately 6.01 mol/L.

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Most popular questions from this chapter

It is quite common for a solid to change from one structure to another at a temperature below its melting point. For example, sulfur undergoes a phase change from the rhombic crystal structure to the monoclinic crystal form at temperatures above \(95^{\circ} \mathrm{C}.\) a. Predict the signs of \(\Delta H\) and \(\Delta S\) for the process \(S_{\text {rhombic }}(s) \longrightarrow S_{\text {monoclinic }}(s).\) b. Which form of sulfur has the more ordered crystalline structure (has the smaller positional probability)?

What information can be determined from \(\Delta G\) for a reaction? Does one get the same information from \(\Delta G^{\circ},\) the standard free energy change? \(\Delta G^{\circ}\) allows determination of the equilibrium constant \(K\) for a reaction. How? How can one estimate the value of \(K\) at temperatures other than \(25^{\circ} \mathrm{C}\) for a reaction? How can one estimate the temperature where \(K=1\) for a reaction? Do all reactions have a specific temperature where \(K=1 ?\)

Cells use the hydrolysis of adenosine triphosphate, abbreviated as ATP, as a source of energy. Symbolically, this reaction can be written as $$\mathrm{ATP}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{ADP}(a q)+\mathrm{H}_{2} \mathrm{PO}_{4}^{-}(a q)$$ where ADP represents adenosine diphosphate. For this reaction, \(\Delta G^{\circ}=-30.5 \mathrm{kJ} / \mathrm{mol}.\) a. Calculate \(K\) at \(25^{\circ} \mathrm{C}\) b. If all the free energy from the metabolism of glucose $$\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(s)+6 \mathrm{O}_{2}(g) \longrightarrow 6 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(l)$$ goes into forming ATP from ADP, how many ATP molecules can be produced for every molecule of glucose? $$\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(s)+6 \mathrm{O}_{2}(g) \longrightarrow 6 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(l)$$ goes into forming ATP from ADP, how many ATP molecules can be produced for every molecule of glucose?

Some water is placed in a coffee-cup calorimeter. When \(1.0 \mathrm{g}\) of an ionic solid is added, the temperature of the solution increases from \(21.5^{\circ} \mathrm{C}\) to \(24.2^{\circ} \mathrm{C}\) as the solid dissolves. For the dissolving process, what are the signs for \(\Delta S_{\mathrm{sys}}, \Delta S_{\text {surr, and }}\) \(\Delta S_{\text {univ }} ?\)

The equilibrium constant \(K\) for the reaction $$2 \mathrm{Cl}(g) \rightleftharpoons \mathrm{Cl}_{2}(g)$$ was measured as a function of temperature (Kelvin). A graph of \(\ln (K)\) versus \(1 / T\) for this reaction gives a straight line with a slope of \(1.352 \times 10^{4} \mathrm{K}\) and a \(y\) -intercept of \(-14.51 .\) Determine the values of \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) for this reaction. See Exercise 79.
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