How many grams of NaCl (molar mass = 58.4 g/mole) must be added to 12.0 g of water (molar mass = 18.0 g/mole) so that Xwater = 0.725?
My answer was 102.69 grams of NaCl. However my friend got 14.8 grams of NaCL. We are not sure who is right? Please respond, and thank you.
I get 14.77 which rounds to 14.8 g NaCl. I can find your error if you want to post your work.
12g x (1mole/18g)= .667 moles H20
.725=(x)/(x + .667)
.725x + .484=x (subtract .725)
.484=.275x
.484/.275=x
1.76=x
1.76moles x (58.4g/1mole)= 102.78g NaCl
Not sure what I'm doing wrong... :(
12g x (1mole/18g)= .667 moles H20 ok
.725=(x)/(x + .667)The error is here. You should have
[mols H2O/(mols H2O + mols NaCl)]=0.725. So it should be [0.667/(0.667 + x)]=0.725.
.725x + .484=x (subtract .725)
.484=.275x
.484/.275=x
1.76=x
1.76moles x (58.4g/1mole)= 102.78g NaCl
Not sure what I'm doing wrong... :(
I hope this helps.
The error in your calculations lies in the setup of the equation for Xwater. When determining the mass of NaCl needed to achieve a desired mole fraction of water (Xwater), the equation should be:
Xwater = (moles of water) / (moles of water + moles of NaCl)
In your calculation, you correctly calculated the moles of water as 0.667, but instead of dividing by the sum of the moles of water and NaCl, you divided by just the moles of water.
The correct equation should be:
0.725 = 0.667 / (0.667 + x)
Solving this equation for x, you get:
0.725(0.667 + x) = 0.667
0.484 + 0.725x = 0.667
0.725x = 0.667 - 0.484
0.725x = 0.183
x = 0.183 / 0.725
x = 0.252 moles
Then, to convert moles to grams, multiply by the molar mass of NaCl:
0.252 moles x 58.4 g/mole = 14.7 grams
Therefore, the correct amount of NaCl that needs to be added is approximately 14.7 grams, not 102.69 grams or 14.8 grams.