Weird: number of moles of NaOH in 20 ml of 1M NaOH

[p3t3r1]

Hi there, this is a not a homework question but rather question about the theory behind this problem.

Say if someone asks you to calculate the number of moles in 20 ml of a 1M NaOH solution, I would usually say it is going to be 20 mmol as you do 20 ml/1000 ml/L x 1M = 0.02 moles = 20 mmol.

However, if you consider the density approach, 1M of NaOH has a density of 1.04 g/ml so 20 ml is 20 x 1.04 g = 20.8 g/40 g/mol (MW of NaOH) that is going to yield 520 mmol of NaOH in 20 mll of 1 M NaOH.

Obviously the density approach give a number that makes no sense. I am just wondering why the density approach is not correct.

Cheers.

 

[Perfection]

1.04 g/ml is the density of the entire solution, most of which is water not NaOH.

 

[varialectio]

Hi there, this is a not a homework question but rather question about the theory behind this problem.

Say if someone asks you to calculate the number of moles in 20 ml of a 1M NaOH solution, I would usually say it is going to be 20 mmol as you do 20 ml/1000 ml/L x 1M = 0.02 moles = 20 mmol.

However, if you consider the density approach, 1M of NaOH has a density of 1.04 g/ml so 20 ml is 20 x 1.04 g = 20.8 g/40 g/mol (MW of NaOH) that is going to yield 520 mmol of NaOH in 20 mll of 1 M NaOH.

Obviously the density approach give a number that makes no sense. I am just wondering why the density approach is not correct.

Cheers.

You are going wrong there, you shouldn't divide by the MW of NaOH. The 20.8g is the weight of the solution, so it makes no sense.

 

[symbolipoint]

Say if someone asks you to calculate the number of moles in 20 ml of a 1M NaOH solution, I would usually say it is going to be 20 mmol as you do 20 ml/1000 ml/L x 1M = 0.02 moles = 20 mmol.

Uncomplicated! You are given 1 Molar NaOH. This is in moles per liter.

However, if you consider the density approach, 1M of NaOH has a density of 1.04 g/ml so 20 ml is 20 x 1.04 g = 20.8 g/40 g/mol (MW of NaOH) that is going to yield 520 mmol of NaOH in 20 mll of 1 M NaOH.

The density is not needed because you already are given the concentration is in moles per liter, and your question was for some number of milliliters; in this case, 0.020 liters. The given and the question do not involve density.

 

[horsecandy911]

As the other posters said, you cannot use the density or volume of the entire solution. If you wanted to take the density approach, you would need to figure out the volume of NaOH in your solution, and multiply that by the density of solvated NaOH. That would give you the mass (which will be much smaller than your 20.8 g), which you could then divide by the molar mass.

The molarity calculations work because molarity is defined as moles SOLUTE/volume SOLUTION, so when you multiply by the volume of a solution it will cancel. In your calculations above, your units will not cancel because you are doing
20.8 g SOLUTION
-----------
40 g NaOH/mol NaOH