68 mL of a 0.28 M CaCl2 solution is added to 92 mL of a 0.46 M CaCl2 solution. Determine the concentration of the combined solution. Show all work with units.

How would you solve this?

Question

68 mL of a 0.28 M CaCl2 solution is added to 92 mL of a 0.46 M CaCl2 solution.  Determine the concentration of the combined solution.  Show all work with units.

How would you solve this?

Henry Antrim · Accepted Answer

The concentration of the combined solution is 0.38 mol/L.

The actions that need to be taken are: 1. The quantity of moles in every solution (a) Initial Solution #"Moles of CaCl"_2 = 0.068 color(red)(cancel(color(black)("L solution"))) × ("0.28 mol CaCl"_2)/(1 color(red)(cancel(color(black)("L solution")))) = "0.0190 mol CaCl"_2# (b) The Second Solution #"Moles of CaCl"_2 = 0.092 color(red)(cancel(color(black)("L solution"))) × ("0.46 mol CaCl"_2)/(1 color(red)(cancel(color(black)("L solution")))) = "0.0423 mol CaCl"_2# Molarity of the combined solutions #"Total moles" = "(0.0190 + 0.0423) mol" = "0.0613 mol"# #"Total volume" = "(68 + 92) mL" = "160 mL" = "0.160 L"# #"Molarity" = "moles"/"litres" = "0.0613 mol"/"0.160 L" = "0.38 mol/L"#

Caleb Adams · Answer

I hope I would solve it correctly.

......I finally get a concentration with respect to #CaCl_2# of #~=0.4*mol*L^-1# As the amount of solute per unit volume, concentration is defined as follows. #"Concentration"="Moles of solute"/"Volume of solution"#. Most of the time we want to assess #"moles of solute"#, and this is simply the product: #"Moles of solute"="Volume"xx"concentration"#. I would get familiar with this expression, because you will use it a lot. To solve your problem (finally!), we solve the quotient:...And in problems such as these we must assume (REASONABLY!) that the volumes are additive. #(0.092*Lxx0.46*mol*L^-1+0.068*Lxx0.28*mol*L^-1)/((92+68)xx10^-3*L)# #~=0.4*mol*L^-1# Do the units in the quotient cancel to give an answer in #mol*L^-1#? It is your problem not mine.

Naomi Aronson · Answer

undefined To determine the concentration of the combined solution, you first need to calculate the total moles of calcium chloride (CaCl2) in each solution, then add them together, and finally divide by the total volume of the combined solutions.

Given:
Volume of Solution 1 (V1) = 68 mL
Concentration of Solution 1 (C1) = 0.28 M

Volume of Solution 2 (V2) = 92 mL
Concentration of Solution 2 (C2) = 0.46 M

Step 1: Calculate moles of CaCl2 in each solution.
For Solution 1:
moles of CaCl2 = concentration (M) × volume (L)
moles of CaCl2 = 0.28 M × (68 mL / 1000 mL/L) = 0.028 moles

For Solution 2:
moles of CaCl2 = concentration (M) × volume (L)
moles of CaCl2 = 0.46 M × (92 mL / 1000 mL/L) = 0.042 moles

Step 2: Add the moles of CaCl2 from both solutions.
Total moles of CaCl2 = 0.028 moles + 0.042 moles = 0.07 moles

Step 3: Calculate the total volume of the combined solution.
Total volume = Volume of Solution 1 + Volume of Solution 2
Total volume = 68 mL + 92 mL = 160 mL

Step 4: Calculate the concentration of the combined solution.
Concentration = Total moles / Total volume
Concentration = 0.07 moles / (160 mL / 1000 mL/L) = 0.4375 M

Therefore, the concentration of the combined solution is 0.4375 M.