---
title: "A student investigates the stepwise hydration of anhydrous calcium chloride, \\(\\text{CaCl}_2(s)\\), at \\(298\\text{ K}\\). The chemical equations and equilibrium constants for the first two hydration steps are given below.  \\[\\text{CaCl}_2(s) + \\text{H}_2\\text{O}(g) \\rightleftharpoons \\text{CaCl}_2\\cdot\\text{H}_2\\text{O}(s) \\quad K_1 = 5.0 \\times 10^3\\] \\[\\text{CaCl}_2\\cdot\\text{H}_2\\text{O}(s) + \\text{H}_2\\text{O}(g) \\rightleftharpoons \\text{CaCl}_2\\cdot 2\\text{H}_2\\text{O}(s) \\quad K_2 = 2.0 \\times 10^2\\]  The overall hydration reaction is represented by the following equation:  \\[\\text{CaCl}_2(s) + 2\\text{H}_2\\text{O}(g) \\rightleftharpoons \\text{CaCl}_2\\cdot 2\\text{H}_2\\text{O}(s) \\quad K_3\\]  Which of the following correctly ranks the equilibrium constants \\(K_1\\), \\(K_2\\), and \\(K_3\\) from greatest to least at \\(298\\text{ K}\\), and gives the correct relationship for \\(K_3\\)?"
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date_modified: "2026-08-23T04:04:25+00:00"
---

# A student investigates the stepwise hydration of anhydrous calcium chloride, \(\text{CaCl}_2(s)\), at \(298\text{ K}\). The chemical equations and equilibrium constants for the first two hydration steps are given below.

\[\text{CaCl}_2(s) + \text{H}_2\text{O}(g) \rightleftharpoons \text{CaCl}_2\cdot\text{H}_2\text{O}(s) \quad K_1 = 5.0 \times 10^3\]
\[\text{CaCl}_2\cdot\text{H}_2\text{O}(s) + \text{H}_2\text{O}(g) \rightleftharpoons \text{CaCl}_2\cdot 2\text{H}_2\text{O}(s) \quad K_2 = 2.0 \times 10^2\]

The overall hydration reaction is represented by the following equation:

\[\text{CaCl}_2(s) + 2\text{H}_2\text{O}(g) \rightleftharpoons \text{CaCl}_2\cdot 2\text{H}_2\text{O}(s) \quad K_3\]

Which of the following correctly ranks the equilibrium constants \(K_1\), \(K_2\), and \(K_3\) from greatest to least at \(298\text{ K}\), and gives the correct relationship for \(K_3\)?

A student investigates the stepwise hydration of anhydrous calcium chloride, \(\text{CaCl}_2(s)\), at \(298\text{ K}\). The chemical equations and equilibrium constants for the first two hydration steps are given below.

\[\text{CaCl}_2(s) + \text{H}_2\text{O}(g) \rightleftharpoons \text{CaCl}_2\cdot\text{H}_2\text{O}(s) \quad K_1 = 5.0 \times 10^3\]
\[\text{CaCl}_2\cdot\text{H}_2\text{O}(s) + \text{H}_2\text{O}(g) \rightleftharpoons \text{CaCl}_2\cdot 2\text{H}_2\text{O}(s) \quad K_2 = 2.0 \times 10^2\]

The overall hydration reaction is represented by the following equation:

\[\text{CaCl}_2(s) + 2\text{H}_2\text{O}(g) \rightleftharpoons \text{CaCl}_2\cdot 2\text{H}_2\text{O}(s) \quad K_3\]

Which of the following correctly ranks the equilibrium constants \(K_1\), \(K_2\), and \(K_3\) from greatest to least at \(298\text{ K}\), and gives the correct relationship for \(K_3\)?

- **A.** \(K_1 > K_2 > K_3\), because \(K_3 = \dfrac{K_1}{K_2}\)
- **B.** \(K_1 > K_3 > K_2\), because \(K_3 = \dfrac{K_1 + K_2}{2}\)
- **C.** \(K_3 > K_1 > K_2\), because \(K_3 = K_1 \times K_2\)
- **D.** \(K_3 > K_1 > K_2\), because \(K_3 = K_1 + K_2\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120301/*