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Chapter 1: Problem 18

What is the calcium concentration of a solution formed by adding \(1 \mathrm{~mol}\) of \(\mathrm{CaCl}_2\) to \(1 \mathrm{~L}\) of distilled water at \(298 \mathrm{~K}\) ? 1\. \(1 M\) 2\. \(1 \mathrm{~m}\) 3\. \(2 M\) 4\. \(2 m\)

Short Answer

Expert verified
1. \(1 M\)

Step by step solution

01

Writing the dissolution equation for CaCl2

When CaCl2 dissolves in water, it dissociates into its constituent ions. The balanced equation for this process is: \[CaCl_2 (s) \rightarrow Ca^{2+} (aq) + 2Cl^- (aq)\] This means that for every 1 mole of CaCl2, 1 mole of calcium ions (Ca^2+) and 2 moles of chloride ions (Cl^-) are produced in the solution.
02

Calculating the initial moles and volume of the solution

We are given that 1 mol of CaCl2 is added to 1 L of distilled water. Thus, we have: Initial moles of CaCl2 = 1 mol We also have the volume of the solution: V = 1 L
03

Calculating moles of calcium ions

As we know from step 1, 1 mole of CaCl2 produces 1 mole of calcium ions (Ca^2+). Therefore, the moles of calcium ions in the solution will be equal to the initial moles of CaCl2. Moles of Ca^2+ = Initial moles of CaCl2 = 1 mol
04

Calculating the molarity of calcium ions

Molarity (M) is defined as the number of moles of solute per liter of solution. We have the moles of calcium ions and the volume of the solution, so we can calculate the molarity as: M = (Moles of Ca^2+) / V M = (1 mol) / (1 L) M = 1 mol/L So, the calcium concentration in the solution is 1 M. Looking at the given options, our answer is: 1. \(1 M\)

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Most popular questions from this chapter

Two blocks of the same density are completely submerged in water. One block has a mass equal to \(m\) and volume equal to \(V\). The other has a mass equal to \(2 m\). What is the ratio of the first block's apparent weight to the second block's apparent weight? 1\. \(1: 1\) 2\. \(1: 2\) 3\. \(2: 1\) \(\begin{array}{lll}\text { 4. } & 4: 1\end{array}\)

An oil drop is stationary within an electric field of \(490 \mathrm{~V} / \mathrm{m}\) that is set up between two parallel plates. If the volume of the oil drop is \(4 \times 10^{-19} \mathrm{~m}^3\), how many excess electrons does it carry? (Note: The fundamental unit of charge \(\mathrm{e}=1.6 \times 10^{-19} \mathrm{C}\).) 1\. \(\quad 1\) 2\. 4 3\. 10 4\. 40

If the separation of the plates is reduced, but the potential difference across them remains constant, which of the following statements must be true? 1\. The electric field increases. 2\. The magnetic field increases. 3\. The capacitance increases. 1\. I only 2\. I and II only 3\. I and III only 4\. II ant III only

A certain metal plate is completely illuminated by a monochromatic light source. Which of the following would increase the number of electrons ejected from the surface of the metal? 1\. Increasing the intensity of the light source 2\. Increasing the frequency of the light source 3\. Increasing the surface area of the metal plate 1\. I only 2\. I and II only 3\. I and III only 4\. II and III only

Which of the following two assumptions is (are) invoked when using a bomb calorimeter to measure energy of combustion? 1\. The system is adiabatic with respect to the environment. 2\. The system maintains an approximately constant pressure throughout the process. 1\. I only 2\. II only 3\. I and II 4\. neither I nor II
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