Calculating HCl Concentration in Solution

[Skw]

Homework Statement

We add 2.7 L of HCl 37% w/w into 97.3L of pure water.
What is the HCl concentration of my final solution in % w/w ?

Relevant Equations

The density of HCl 37% w/w is 1.18 kg/L.

1% or 1.18 % (w/w) ?

 

[dextercioby]

Must be some lingo issue, but what is "w/w"?

 

[Skw]

w/w means by weight/weight

 

[dextercioby]

How does your textbook define concentration? Units are also a hint.

 

[Skw]

No definition

 

[dextercioby]

I suspect they refer to https://en.wikipedia.org/wiki/Concentration mass concentration, which is measured in SI (typically as) grams of substance (in this case HCl) per liter of solution.
How can you find the mass of HCl? What about the quantity of solution?

 

[Skw]

https://www.laboratorynotes.com/molarity-of-37-percent-hydrochloric-acid-hcl/

In this link it defines what is a 37% HCl w/w

 

[dextercioby]

So you think you're looking for molarity? (nr of moles of HCl per l) Anyway, start showing some calculations, please.

 

[Skw]

2.7L in 97.3L corresponds to a dilution of 1/37 v/v (volume/volume)
To prepare a 1% w/w solution : We need 1/37 kg = 0.027 kg
so with a density of 1.18 kg/L: 0.027/1.18=2.3% v/v
For a 1% w/w HCl solution we need to dilute the stock 2.3% v/v.

However, it was diluted 2.7%.
The final solution is therefore 1.18% HCl w/w.

 

[Borek]

The final solution is therefore 1.18% HCl w/w.

That is the correct answer, but to be honest I have troubles following your calculations.

To prepare a 1% w/w solution : We need 1/37 kg = 0.027 kg

You left out so much information it doesn't make sense. Not only I have no idea 0.027 kg of what, but also I am perfectly sure you can prepare 1%w/w solution starting with 1 kg (no matter whether it is mass of just HCl or the solution). So apparently there are some unstated assumptions here, and I not a remote mind reader to know what they are

Besides, I am not convinced what you did is in general a correct approach. Using %v/v is a potential problem, as volumes are not additive.

The simplest correct approach is to calculate separately mass of the HCl and mass of solvent in both mixed volumes, sum them up and use these numbers to calculate final %w/w concentration. Masses are additive, so you don't have to worry about contraction.

 

[Skw]

Ok thank you !

Sorry my calculation wasn’t clear, I first reasoned as if it would be 37% v/v and I thought the 1% was the good answer, but then I realised it was w/w so that the good answer was 1.18%.

As you suggested, a simpler calculation could be the following:

2.7L at 1.18 kg/L = 2.7*1.18 = 3.186 kg
In this total weight, 37% is HCl: 3.186*0.37 = 1.1788 kg of HCl
In the total final solution, the weight is: 97.3 kg + 3.186 = 100.49 kg
So in the solution there is 1.178 kg HCl / 100.49 kg total = 0.0118 = 1.18% w/w

 

[mjc123]

I get 1.17% to 3 sig figs.

 

[Borek]

I get 1.17% to 3 sig figs.

Yep. Missed that as I got the result from the mixing calculator which for HCL solutions uses density tables for 20°C, so 0.9982 g/mL, and the result listed was 1.1787:

But technically the correct answer is 1.2% (2.7L at 37%, so two significant digits).

 

[symbolipoint]

Homework Statement: We add 2.7 L of HCl 37% w/w into 97.3L of pure water.
What is the HCl concentration of my final solution in % w/w ?
Relevant Equations: The density of HCl 37% w/w is 1.18 kg/L.

1% or 1.18 % (w/w) ?

I suggest look in reference book for density or specific gravity for 37% w/w HCl.
----OOHHHHH, good! You found something....

...and I am obviously very late finding this topic.