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Material balances question

A certain type of fern has been shown to effectively extract arsenic from soils. In one experiment, the ferns (containing 5 ppm arsenic) were grown for two weeks in normal soil which originally contained 6 ppm arsenic. After the 2 weeks, the arsenic in the soil dropped to 5 ppm and the ferns were analyzed and found to contain 755ppm of arsenic. What is the ratio of soil mass to plant mass?

A certain amount of arsenic left the soil and ended up in the ferns. That amount of arsenic represented 1 ppm of the mass of the soil (because the soil changed from 6ppm to 5ppm over the two week period). Meanwhile, that same amount of arsenic represented 750ppm of the mass of the plant (because of the change from 5ppm to 755ppm). So what's that ratio?

so would that mean that it would be (5/755)x=(6/5)
x=906 parts per soil per 5 parts plant?

Never mind. I'm retarded, its 750

Quote:

Originally Posted by linedpaper92

so would that mean that it would be (5/755)x=(6/5)
x=906 parts per soil per 5 parts plant?

You're close, but instead of division you should just be doing subtraction.

(755-5)x = (6-5)

That gives you the net change in concentration in each medium, which is what's important here. I know this might seem a little strange, since with ratio problems you usually end up setting two different fractions equal to each other. If it makes more sense to you to do it that way, you'd set it up like this:

$\frac{\text{Arsenic mass absorbed by plant}}{\text{plant mass}}=\frac{755-5}{1000000}$

$\frac{\text{Arsenic mass removed from soil}}{\text{soil mass}}=\frac{6-5}{1000000}$

The factor of 1000000 comes about because the concentration is in parts per million. Had it been given in percent, it would have been a factor of 100 instead.

Meanwhile, since the mass of arsenic removed from the soil is exactly equal to the mass absorbed by the ferns, we can just use the soil absorption for both. Rewriting the two concentration equations, that results in:

$\frac{\text{Arsenic mass absorbed by plant}}{\text{plant mass}}=\frac{750}{1000000}$

$\frac{\text{Arsenic mass absorbed by plant}}{\text{soil mass}}=\frac{1}{1000000}$

Now if we simply divide the first equation by the second, the arsenic mass and the factor of 1000000 cancel out, and we're left with:

$\frac{\text{soil mass}}{\text{plant mass}}=\frac{750}{1}= 750$

Note that that's the same answer you'd get if you solve for x in the equation at the top of this post.

Quote:

Originally Posted by linedpaper92

never mind. I'm retarded, its 750

LOL! I see you got there on your own. Good job!