# Video: Calculating the Volume of Water Required to Dilute a Given Volume of HCl Solution of Known Concentration to a Given, Lower Concentration

To dilute 25 mL of a 4 M HCl solution to 1 M, the volume of water required is ＿. [A] 25 mL [B] 50 mL [C] 75 mL [D] 100 mL [E] 150 mL

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### Video Transcript

To dilute 25 millilitres of a four-molar HCl solution to one molar, the volume of water required is blank. A) 25 millilitres, B) 50 millilitres, C) 75 millilitres, D) 100 millilitres, or E) 150 millilitres.

So what we have is a four-molar hydrochloric acid solution. And what this means is that, for each litre of solution we have, we’d have four moles of hydrochloric acid. And we have 25 millilitres. 1000 millilitres is equivalent to a litre.

In this scenario, we want to take this 25 millilitres of solution and dilute it down with more solvent, in this case water, until the concentration of hydrochloric acid is only one molar. What we need to find is the volume of water we need to add to the liquid to make the final concentration one molar.

Now we need to be careful here not to work out the total volume. We just need to work out the difference between the starting volume and the final volume. To help us along the way, we can use the dilution equation, which details the relationships between the concentration and volume of our final solution and the concentration and volume of our initial solution. If you can’t remember the dilution equation, you can derive it.

We know amount is equal to concentration times volume. When we do a dilution, the amount doesn’t change. Meaning that the concentration times the volume before must be equal to the concentration times the volume after dilution. Now let’s rearrange the equation in terms of the final volume. The final volume is equal to the initial concentration multiplied by the initial volume all divided by the final concentration. This gives us four molar divided by one molar multiplied by 25 millilitres.

All the options for final answers are in millilitres. So we don’t need to convert millilitres to litres. Instead, we just get our final volume as 100 millilitres. This makes sense. If we want to reduce the concentration to a fourth of its original value, then we have to have four times as much solution. All that remains is to work out the diluting volume, which is the final volume minus the initial volume, which is 100 minus 25, which is 75 millilitres.