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35.6g of NaOH is dissolved in 150g of 20% NaOH solution. What is the density od the solution?

I have tried solving this problem, but I 've come across a few obstacles.

Firstly, I found the mass of NaOH in the original solvent which is 30g. The added NaOH weighs 35.6g, meaning there is ultimately 75.6g of NaOH, and that the mass of the solution is 185.6g. The next step would be to find the density of the solution, but this requires the volume of the solution, that is not given in the problem. I also tried to calculate the number of moles to later calculate V using the formula V=n*Vm, but I am not sure how to calculate the molar mass(M) of the solution.I am not sure if I am to use H2O or NaOH.

Can someone tell me if I am going in the right direction and if my calculations are even in the right direction, and if not, what is the right one?

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  • $\begingroup$ You cannot determine solution density from its percentage. It is experimental parameter. For common substances, it is measured, interpolated and tabelated. $\endgroup$
    – Poutnik
    Aug 8, 2022 at 16:40
  • $\begingroup$ does this mean that the task cannot be solved with the given data? $\endgroup$
    – qalquta888
    Aug 8, 2022 at 16:44
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    $\begingroup$ Even if solution densities were linear functions of mass percentages - but they are not - you would need at least densities of pure substances. // All depends on if you are allowed and/or supposed to use additional data sources, like density tables. $\endgroup$
    – Poutnik
    Aug 8, 2022 at 17:08
  • $\begingroup$ There is one possible task solution, relying on incorrect percentage usage by the task author, assuming 20% means 20 g / 100 mL of solution. Or even worse, 20 g / 100 mL of water. $\endgroup$
    – Poutnik
    Aug 8, 2022 at 18:42
  • $\begingroup$ This question looks a lot like this one. If you have created a new user account to circumvent a ban, you are in violation of the terms and policies of the site. $\endgroup$
    – Todd Minehardt
    Aug 8, 2022 at 19:54

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You can simplify your problems by looking at the published tables. As you have been explained in the comments, predicting densities is not an easy job and I don't know if it can even be predicted.

This link provides the densities of NaOH solution as a function of mass percentage. https://wissen.science-and-fun.de/chemistry/chemistry/density-tables/density-of-sodium-hydroxide/

Plot the data in Excel and generate a function. Calculate the final mass percentage of your solution.

Your first step is correct, i.e., the initial solution contains 30 g of NaOH, then you add 35.6 g to the solution. The total mass of the solution is 185.6 as you correctly calculated. What is the final mass percentage? 65.6 g NaOH/ 185.6 g solution. This is around 35% wt/wt NaOH. Roughly, interpolating from the given table, the density should be around 1.39!

Commas in German data are equivalent to decimals in English, so mass percentage of 5,5 means 5.5.

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