A 200. gram sample of a salt solution contains 0.050 grams of NaCl. What is he concentration of the solution in parts per million?

Question

a)50. ppm
b)250. ppm
c)2.5 * 10^-4 ppm
d)5.0 * 10^4 ppm

Answer 1

You can do this one of several ways.
ppm means parts per million.
0.05 g NaCl/200 g sample.

#1.
0.05g NaCl/200 g soln = 2.5E-4g NaCl/g soln. Now must multiply numerator and denominator by 1E6 (a million) to give you
2.5E-4*1E6 g NaCl/1E6 g soln = 2.5E2/1E6 g soln = 250 ppm.

#2.
Scale it up by units.
0.05 gNaCl/200 g soln. Multiply by 5 to obtain g NaCl/1000 g soln
0.05*5/200*5 = 0.25 g NaCl/1000 g soln
Now multiply by 1000 to get to a million.
0.25*1000 g NaCl/1000*1000g soln = 250 g NaCl/1,000,000 g soln = 250 ppm.

#3. You do #2 in one step.
0.05g NaCl/200 g soln = 0.05*x/(200*x)
What must x be to get to 1,000,000. That is 1,000,000/200 = 5,000 so multiply both numerator and denominator by 5,000.
0.05*5000 g NaCl/200*5000 =
250 g NaCl/1,000,000 = 250 ppm.