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Chapter 12: Problem 105

You have \(2500.0 \mathrm{~mL}\) of a \(0.250 \mathrm{M}\) solution of \(\mathrm{NaCl}\). (a) How many moles of \(\mathrm{NaCl}\) are present in this solution? (b) How many moles of ions are present in this solution? (c) How many grams of \(\mathrm{NaCl}\) would you recover if you evaporated all of the water off of this solution?

Short Answer

Expert verified
(a) To calculate the moles of NaCl, we use the given molarity and volume of the solution: \(\text{moles of NaCl} = (0.250\: M) * (2.5\: L) = 0.625 \: \text{moles}\) (b) As each mole of NaCl produces two moles of ions, we multiply the moles of NaCl by 2: \(\text{moles of ions} = 2 * 0.625 \: \text{moles} = 1.25 \: \text{moles}\) (c) To find the mass of NaCl, we multiply the moles of NaCl by its molar mass: \(\text{mass of NaCl} = 0.625 \: \text{moles} * 58.44\: \mathrm{g/mol} = 36.525\: \mathrm{g}\)

Step by step solution

01

(Step 1: Calculate the number of moles of NaCl using molarity)

The molarity of a solution is defined as the number of moles of solute per liter of solution. It's given in the problem that we have a 0.250 M NaCl solution. We can use the formula: Molarity (M) = moles of solute / volume of solution (in liters) We need to first convert the volume of the solution from milliliters to liters: 1 L = 1000 mL Now we can use the molarity to find the moles of NaCl. \((a)\) \(0.250 M = \frac{\text{moles of NaCl}}{2.5\: L}\) Solving for moles of NaCl: \(\text{moles of NaCl} = (0.250\: M) * (2.5\: L)\)
02

(Step 2: Find the number of moles of ions in the NaCl solution)

\(\mathrm{NaCl}\) dissociates in water to form one sodium ion (\(\mathrm{Na^+}\)) and one chloride ion (\(\mathrm{Cl^-}\)). Therefore, for every mole of \(\mathrm{NaCl}\), there are two moles of ions (one mole of \(\mathrm{Na^+}\) and one mole of \(\mathrm{Cl^-}\)). To find the total number of ions in moles, we need to multiply the result from step 1 by 2. \((b)\) \(\text{moles of ions} = 2 * \text{moles of NaCl}\)
03

(Step 3: Calculate the mass of NaCl that can be recovered)

We can find the mass of NaCl that can be recovered by using the relationship between moles and mass. The molar mass of NaCl is: \(\mathrm{NaCl:} \: 58.44\: \mathrm{g/mol} \) Multiply the moles of NaCl obtained in step 1 by the molar mass of \(\mathrm{NaCl}\) to find the mass of NaCl that can be recovered. \((c)\) \(\text{mass of NaCl} = \text{moles of NaCl} * 58.44\: \mathrm{g/mol} \) Now we will put everything together and calculate the answers.

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Most popular questions from this chapter

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