Calculating mass of a substance in solution

[life-is-full-of-questions]

Hello everyone!

I am new to chemistry and am working on a question that I got stuck on. If anyone could help me to continue my work, it would be greatly appreciated.

The chemist used a solution of lead nitrate, Pb(NO₃)_2, with a concentration of 0.025 mol l^-1. If they were preparing one litre of this solution, what mass of lead nitrate should they weigh out?

For the initial calculations, I used the relative atomic mass (RAM) for each element and got the result for : RMM Pb(NO₃)₂ = 331

The relative molecular mass of lead nitrate is 331.

The mass of one molecule of lead nitrate is 331 g.

The molar mass of lead nitrate is 331 g mol^-1.

I was supposed to use this equation (as that is the only one we were shown, but I am not sure how:

Mass of a substance = (number of moles of substance) x (molar mass of substance)

The concentration mol l^-1 is throwing me off too, as surely the mass needs to be in grams in the end.

Can anyone advise me on this matter?

Thank you in advance

Edited May 25, 2021 by life-is-full-of-questions

[exchemist]

29 minutes ago, life-is-full-of-questions said:

Hello everyone!

I am new to chemistry and am working on a question that I got stuck on. If anyone could help me to continue my work, it would be greatly appreciated.

The chemist used a solution of lead nitrate, Pb(NO₃)_2, with a concentration of 0.025 mol l^-1. If they were preparing one litre of this solution, what mass of lead nitrate should they weigh out?

For the initial calculations, I used the relative atomic mass (RAM) for each element and got the result for : RMM Pb(NO₃)₂ = 331

The relative molecular mass of lead nitrate is 331.

The mass of one molecule of lead nitrate is 331 g.

The molar mass of lead nitrate is 331 g mol^-1.

I was supposed to use this equation (as that is the only one we were shown, but I am not sure how:

Mass of a substance = (number of moles of substance) x (molar mass of substance)

The concentration mol l^-1 is throwing me off too, as surely the mass needs to be in grams in the end.

Can anyone advise me on this matter?

Thank you in advance

OK. So, on the right hand side,  you know the molar mass. The other thing you need to know is the number of moles of substance, right? 

How many moles would there be in one litre of the solution, at that concentration? 

[life-is-full-of-questions]

4 hours ago, exchemist said:

OK. So, on the right hand side,  you know the molar mass. The other thing you need to know is the number of moles of substance, right? 

How many moles would there be in one litre of the solution, at that concentration? 

0.025 mol l^-1 is 0.025 mol/litre, so 0.025 mol in 1 litre. But if I multiplied :

Mass of a substance = 0.025 mol l^-1 x 331 g mol^-1 

It would not give the correct answer, as the mol/l s do not cancel each other, like they would in a division, and it would not result in grams. Or am I so tired, that I cannot think clearly anymore? Sorry.

[studiot]

I suppose it boils down to what you have been taught about moles.

5 hours ago, life-is-full-of-questions said:

The relative molecular mass of lead nitrate is 331.

The mass of one molecule of lead nitrate is 331 g.

The first line is true

The second is not.

 

331 is a pure number that has no units because it is the ratio of two masses.

 

Tha mass of one gram-mole of substance (lead(II) nitrate in this case) is 331 grammes.

 

So if N is the pure number of gram-moles in one litre of solution,

Then the mass in one litre of solution is N times the mass of one gram-mole.

 

So you would weigh out how many grammes ?

 

As a matter of practical interest, since chemistry is a practical subject, how would you make up exactly one litre of solution ?

[exchemist]

43 minutes ago, life-is-full-of-questions said:

0.025 mol l^-1 is 0.025 mol/litre, so 0.025 mol in 1 litre. But if I multiplied :

Mass of a substance = 0.025 mol l^-1 x 331 g mol^-1 

It would not give the correct answer, as the mol/l s do not cancel each other, like they would in a division, and it would not result in grams. Or am I so tired, that I cannot think clearly anymore? Sorry.

mol/litre x g/mol DOES cancel. And gives you an answer in g/litre. Which actually is OK since you've been asked to work this out for a litre, i.e. on a per litre basis. 

But in fact, to be pedantic, I asked you to consider how many moles there would be in one litre, the answer to which is "0.025 moles", not "0.025mol/l". So you can plug that into your equation, can't you?  

You've nearly got this, so don't fall at the last fence. Have confidence! 

Edited May 25, 2021 by exchemist

[life-is-full-of-questions]

4 hours ago, exchemist said:

mol/litre x g/mol DOES cancel. And gives you an answer in g/litre. Which actually is OK since you've been asked to work this out for a litre, i.e. on a per litre basis. 

But in fact, to be pedantic, I asked you to consider how many moles there would be in one litre, the answer to which is "0.025 moles", not "0.025mol/l". So you can plug that into your equation, can't you?  

You've nearly got this, so don't fall at the last fence. Have confidence! 

Oh, I think I get it. So 

Number of moles of substance is 0.025 mol

Molar mass of substance is 331 g mol^-1

Mass of a substance = (number of moles of substance) x (molar mass of substance)

Mass of substance = 0.025 mol x 331 g mol^-1

=8.275 g, as the mols cancel out.

I hope this is it now. 

[exchemist]

10 hours ago, life-is-full-of-questions said:

Oh, I think I get it. So 

Number of moles of substance is 0.025 mol

Molar mass of substance is 331 g mol^-1

Mass of a substance = (number of moles of substance) x (molar mass of substance)

Mass of substance = 0.025 mol x 331 g mol^-1

=8.275 g, as the mols cancel out.

I hope this is it now. 

Looks OK to me.

Just remember the -1 superscript means "per" whatever the unit is. You may find if you rewrite it as a "/" it is easier to see what cancels.

And try not to just follow the formula you have been given mechanically, but think what you are trying to do, i.e. the number of moles in a certain volume of solution and then then the number of grams that corresponds to.