Concentration of NaOH Solution: Calculation and Analysis

[gt000]

Homework Statement

A student added 50.0mL of an NaOH solution to 100.0 mL of 0.400 M HCL. The solution was then treated with an excess of aqueous chromium (III) nitrate, resulting in formation of 2.06g of precipitate. Determine the concentration of the NaOH solution.

Homework Equations

pH=14-pOH

The Attempt at a Solution

NaOH + HCL -> NaCL +H₂O
Cr(NO₃)₃ + HCL -> Cr(OH)₃ + 3NaNO₃

I'm not sure what to do after creating the equations. I tried to use the 2.06g and converting this to moles using the molar weight of 3NaNO₃, but i think I'm not doing the right steps. Any help?

 

[chemisttree]

Cr(NO₃)₃ + HCL -> Cr(OH)₃ + 3NaNO₃

You probably meant this...

Cr(NO₃)₃ + NaOH ---> Cr(OH)₃ (s) + 3NaNO₃ (aq)

 

[gt000]

Yea I forgot to put the solid and aqueous. I'm still not really sure what to do, but I'll try it again and see if i get an answer.

 

[Borek]

Look at the reaction equation now - what is the substance that precipitated and weights 2.06 g?

 

[gt000]

Cr(NO3)₃ + 3NaOH ---> Cr(OH)₃ (s) + 3NaNO₃ (aq)

2.06g/103g = 0.02 mol Cr(OH)₃
Cr(OH)₃ * (1 mol NaOH/3 mol Cr(OH)₃) = 0.0067 mol NaOH
Molary of NaOH =.0067 Mol/.05L = .133 M NaOH

I wrote the right equation this time. Here's my attempt, but I'm not sure if its correct.

 

[Borek]

You are partially right. First, your molar mass of chromium (III) nitrate is wrong. Second, you have calculated amount of excess NaOH that was left after it was partially neutralized with HCl, but you have neglected the neutralization.

 

[gt000]

Am I not suppose to use Chromium (III) Hydroxide's molar mass? Isn't that compound the one that has precipitated?

Ok so another attempt:
After I obtained .02 ml Cr(OH)₃, I multiplied by 3 instead of dividing because the ratio is 3:1 not 1:3.
0.02 x 3 = 0.06 moles NaOH
Since there needs to be neutralization with excess:
0.1L x 0.4 M = 0.04 moles HCl.
NaOH and HCl both have the same ratio of 1:1.
0.06 moles + 0.04 moles = 0.1 moles
0.1 moles/0.05 L = 2 M NaOH.

 

[Borek]

Am I not suppose to use Chromium (III) Hydroxide's molar mass? Isn't that compound the one that has precipitated?

Sorry, my mistake. You are OK this time.