How Much Distilled Water to Add for Dilution Using c1v1 = c2v2?

[Ace.]

Homework Statement

Determine how much distilled water must be added to 250 ml of a 1.5 M solution of Na₂CO₃ to dilute it to a concentraion of 0.5 M.

Homework Equations

c1v1=c2v2

The Attempt at a Solution

I'm having trouble understanding how to identify c1,v1,c2, and v2, especially since every question is worded differently. My guess is that v1 = 250mL, c1 = 1.5 M, and c2 = 0.5 M. And we're solving for v2...? My teacher didn't explain this very well so is there any rule for this law? Because for example I know that c1 and c2 can't be used interchangeably so how do I know which is c1 and which is c2?

 

[symbolipoint]

Just pick a subscript number to identify each solution (meaning each liquid).

Let the starting, more concentrated solution be "1", and the diluted solution be "2".
The concentrated starting solution is C₁=1.5 molar, V₁=0.25 liters.
The diluted solution is C₂=0.5 molar, V₂=0.25 liters + Q.
I'm choosing Q to be the volume of water to add to the 250 ml. of stock Na2CO3 solution to make the dilution.

The process of planning runs that way because the objective is to make a dilution; thinking of it this way is just easier for ME. If you wanted, you could just use C₁V₁=C₂V₂ as you did, but then you'd finish by finding the difference in volume.

 

[epenguin]

So many of the quantitative questions in elementary chemistry are just arithmetic simple proportion I am often surprised by how heavy weather many students make of them. My guess is that it is because students segment knowledge. One thing comes up in arithmetic lessons and the same thing in chemistry lessons, and they are thought to have nothing to do with each other.

You are asked to make a solution one third as concentrated as before by adding water. So you make the volume containing the stuff three times what it was before - add twice the volume of water, that is 500ml.

Simples.

You can also use a formula.

 

[Borek]

Because for example I know that c1 and c2 can't be used interchangeably so how do I know which is c1 and which is c2?

Usually we use C₁V₁ for the solution that is being diluted and C₂V₂ for the solution after dilution. But it doesn't matter. All that matters is that you are consistent in using indexes. C₁ and V₁ must describe the same solution (be it final or the one being diluted) and C₂ & V₂ must describe the other solution.