Calculate the cost of one pound of nitrogen from a fertilizer containing 30.0 % sodium nitrate by weight and costing $9.00 per 100 lb. Express your answer in dollars per pound of nitrogen to three significant figures.

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