A sample of 9.4 grams of NaOH is dissolved into 693 mL of aqueous 0.250 M NaOH (assume no volume change). This solution is then poured into 2.37 gallons of water. (You may assume that the two volumes can be added.) What is the concentration of NaOH in the final solution?
Answer in units of M.
Okay heres my work:
9.4/40(MM)= .235
.250x .693=.17325
added togehter= .40825
2.37 gallons= 8971.4259 mL
.40825/8971.4259= .000045506 but my answers wrong.
Okay heres my work:
9.4/40(MM)= .235
The 0.235 mole is correct.
.250x .693=.17325
This is OK.
added togehter= .40825
This is OK (except for the typo on together :-)).
2.37 gallons= 8971.4259 mL
This is OK.
.40825/8971.4259= .000045506 but my answers wrong.
Two things wrong here. First you didn't add the 693 mL to the 8971 mL AND you didn't convert mL to L. M = moles/L, not moles/mL. Making those two corrections should take care of it.
To find the concentration of NaOH in the final solution, you need to consider the total amount of NaOH and the total volume of the solution.
First, let's start with the initial amount of NaOH: you correctly calculated that the mass of NaOH is 9.4 grams, and its molar mass (MM) is 40 g/mol. Dividing the mass by the molar mass gives you:
9.4 g / 40 g/mol = 0.235 moles of NaOH
Next, you calculated the initial volume of the solution to be 693 mL and the initial concentration of NaOH to be 0.250 M. Multiplying the volume by the concentration gives you:
0.250 mol/L x 0.693 L = 0.17325 moles of NaOH
To find the total moles of NaOH, you need to add the moles from the mass and the moles from the concentration:
0.235 moles + 0.17325 moles = 0.40825 moles
Now, let's consider the final volume of the solution. You mentioned that you poured the initial solution into 2.37 gallons of water, which can be converted to milliliters as you did:
2.37 gallons x 3785 mL/gallon = 8971.4259 mL (rounded to 4 decimal places)
To find the final concentration of NaOH in the solution, divide the total moles of NaOH by the final volume:
0.40825 moles / 8971.4259 mL = 0.0000455 moles/mL
However, we want the concentration in units of moles per liter (M), not moles per milliliter. To convert, multiply by 1000 to get moles per liter:
0.0000455 moles/mL x 1000 mL/L = 0.0455 M
Therefore, the concentration of NaOH in the final solution is 0.0455 M.