Answer:
1.82 lb
Explanation:
Given that:
The chemical formula for sodium nitrate is NaNO₃, thus its molar mass = 84.99 g/mole
Also, the atomic mass of Nitrogen (N) = 14 g/mole
Thus; the mass of N in NaNO₃ = (14/84.99) × 100
the mass of N in NaNaNO₃ = 16.473 %
The cost of the fertilizer = $9.00/100 lb
Hence, for one pound of Nitrogen(N) from the fertilizer containing NaNO₃; we have:
= 100/16.473 lb of NaNO₃
= 6.0705 lb of NaNO₃
Given that the fertilizer contains 30% of NaNO₃
The needed amount of fertilizer = 6.0705 × (100/30)
The needed amount of fertilizer =20.235 lb
Thus the cost of one pound of nitrogen from the fertilizer is:
= ( $9.00/100 lb ) × 20.235 lb
= 1.82 lb
To calculate the cost of one pound of nitrogen from this fertilizer is $1.82
Given the following data:
Note: Sodium nitrate = [tex]NaNo_3[/tex]
Molar mass of [tex]NaNo_3[/tex] = 84.99 g/mol.
Atomic mass of nitrogen (N) = 14.00 g/mol.
To calculate the cost of one pound of nitrogen from this fertilizer:
First of all, we would determine the mass of nitrogen contained in sodium nitrate.
[tex]Mass \;of \;N = \frac{14}{84.99} \times 100\\\\Mass \;of \;N = \frac{1400}{84.99}[/tex]
Mass of N = 16.47 grams.
Next, we would find a pound of nitrogen in the fertilizer:
[tex]One\; pound \;of\;N = \frac{100}{16.47}[/tex]
One pound of nitrogen = 6.07 lb of [tex]NaNo_3[/tex]
Also, we would calculate the amount of nitrogen in [tex]NaNo_3[/tex] required from the fertilizer.
[tex]Amount \;of\;N = \frac{100}{30} \times 6.07\\\\Amount \;of\;N = \frac{607}{30} \\\\Amount \;of\;N = 20.2\;lb[/tex]
Now, we can calculate the cost of one pound of nitrogen from this fertilizer:
[tex]Cost = \frac{9.00}{100} \times 20.2\\\\Cost = \frac{181.8}{100} \\\\Cost = 1.818[/tex]
To three significant figures:
Cost = $1.82
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