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Chapter 4: Problem 92

A \(230 .-\mathrm{mL}\) sample of a \(0.275-M \mathrm{CaCl}_{2}\) solution is left on a hot plate overnight; the following morning, the solution is \(1.10 M\). What volume of water evaporated from the \(0.275 \mathrm{M} \mathrm{CaCl}_{2}\) solution?

Short Answer

Expert verified
The volume of water evaporated from the \(0.275\,M\) CaCl2 solution is \(0.1725\,L\) or \(172.5\,mL\).

Step by step solution

01

Determine the initial moles of CaCl2

To find the initial moles of CaCl2, use the formula moles = volume × concentration, where the volume must be in liters. Given, volume = 230 mL, and concentration = 0.275 M. Convert the volume from milliliters to liters. \(Volume_{Initial} = \frac{230}{1000}\) L \(Volume_{Initial} = 0.230\) L Now, calculate the initial moles of CaCl2. \(Moles_{Initial} = Volume_{Initial} × Concentration_{Initial}\) \(Moles_{Initial} = 0.230L × 0.275M \) \(Moles_{Initial} = 0.06325 mol\)
02

Calculate the final volume of the solution

Since the moles of CaCl2 remain the same, we can now find the final volume of the solution using the final concentration. Use the formula volume = moles/concentration. \(Volume_{Final} = \frac{Moles_{Initial}}{Concentration_{Final}}\) \(Volume_{Final} = \frac{0.06325\,\text{mol}}{1.10\,M}\) \(Volume_{Final} = 0.0575\) L
03

Find the volume of the water evaporated

Now that we have the final volume of the solution, we can find the volume of the water evaporated using the difference between the initial and final volumes. \(Volume_{Evaporated} = Volume_{Initial} - Volume_{Final}\) \(Volume_{Evaporated} = 0.230\,L - 0.0575\,L\) \(Volume_{Evaporated} = 0.1725\) L The volume of water evaporated from the \(0.275\,M\) CaCl2 solution is \(0.1725\,L\) or \(172.5\,mL\).

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