In a group assignment, students are required to fill 10 beakers with [tex]$0.720 M CaCl _2$[/tex]. If the molar mass of [tex]$CaCl _2$[/tex] is 110.98 g/mol and each beaker must have [tex]$250 . mt$[/tex] of solution, what mass of [tex]$CaCl _2$[/tex] would be used?
Use molarity [tex]$=\frac{\text { moles of solute }}{\text { Iters of solution }}$[/tex].
Answer (2)
Convert the volume of solution in each beaker to liters: 250 m L = 0.250 L .
Calculate the number of moles of C a C l 2 in each beaker: 0.720 M × 0.250 L = 0.18 m o l es .
Determine the mass of C a C l 2 in each beaker: 0.18 m o l es × 110.98 g / m o l = 19.9764 g .
Calculate the total mass of C a C l 2 for 10 beakers: 10 × 19.9764 g = 199.764 g . The final answer is 200 g .
Explanation
Problem Setup We are given that there are 10 beakers, each filled with 250 mL of a 0.720 M C a C l 2 solution. The molar mass of C a C l 2 is 110.98 g/mol. We need to find the total mass of C a C l 2 used.
Volume Conversion First, let's find the volume of solution in each beaker in liters: V = 250 m L = 0.250 L
Calculating Moles per Beaker Next, we calculate the number of moles of C a C l 2 in each beaker using the molarity formula: Molarity = liters of solution moles of solute moles of solute = Molarity × liters of solution moles of C a C l 2 = 0.720 M × 0.250 L = 0.18 m o l es
Calculating Mass per Beaker Now, we find the mass of C a C l 2 in each beaker using the molar mass: mass = moles × Molar mass mass of C a C l 2 = 0.18 m o l es × 110.98 g / m o l = 19.9764 g
Calculating Total Mass Finally, we calculate the total mass of C a C l 2 needed for all 10 beakers: Total mass = 10 × mass per beaker Total mass = 10 × 19.9764 g = 199.764 g Rounding to the nearest whole number, we get approximately 200 g.
Examples
Imagine you're a chemist preparing solutions for an experiment. This problem is similar to calculating how much of a chemical you need to dissolve in water to get the right concentration for your reactions. Knowing how to calculate molarity and mass is crucial for accurate and repeatable experiments. For example, if you're preparing a specific concentration of a salt solution to study its effect on plant growth, you need to calculate the exact mass of salt to dissolve in a given volume of water. This ensures that each plant receives the same concentration, allowing for a fair comparison of results.
In total, you will need approximately 200 g of CaCl 2 for the 10 beakers, each holding 250 mL of a 0.720 M solution. This is calculated using the molarity formula to determine moles of solute and then converting that to mass. Each step involves converting volume to liters, calculating moles per beaker, finding the mass per beaker, and finally calculating the total mass for all beakers.
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