[artwill872]

The following is a word problem that I was given to solve. It seems pretty straight forward but I don't think I solved it properly. I have no way of getting immediate feedback and I'd like some.

I'm going to show the problem and then beneath it briefly explain my work.
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A chemical company mixes aqueous ammonia (NH₃) and aqueous carbon dioxide (CO₂) to create aqueous urea (CH₄N₂O) and water.

A batch of urea weighed 168.4 kg. The company claims they usually have a percentage yield of 70.0%. They have also determined 38.26kg of carbon dioxide is left over after the reaction was completed.

Determine if the company is making a profit or taking a loss given the following information.

Chemical - Price ($/metric ton)(1 metric ton=1000kg)
Ammonia - $325
Carbon dioxide - $50
Urea - $425

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I started by writing a balanced equation:
4 NH3 + 2 CO2 ---> 2 CH4N2O + 2 H2O

The problem made it clear that ammonia was the limiting reagent in the reaction, so I first tried to determine how much ammonia would be necessary to produce the 168.4kg of urea.

Using stoichiometric relationships in the balanced equation that I created, I determined that this amount was 95.50704kg NH3.

Then I wanted to determine how much CO2 would be required to react with this amount of NH3. The amount that I got for CO2 was 123.407kg (and I added the 38.26kg from the word problem to get the total amount used in the reaction. This amounted to 161.67kg of CO2 in total).

I then took the amounts in kg (95.507kg NH3, 161.67kg CO2, and 168.4kg CH4N2O), divided each of them by 1000, and multiplied them by the $ amount specified in the price chart.

The final answer was that the company made a profit on this batch of urea of $32.45.

Though, I feel like I overlooked something. Any feedback?

[DrCMS]

Though, I feel like I overlooked something. Any feedback?

You missed this bit

The company claims they usually have a percentage yield of 70.0%.

[artwill872]

I figured that that might have been the case. But I wasn't quite sure how to use this information. I'm pretty sure that I could determine the theoretical yield by solving for X in the following equation:

168.4
-----  x 100 = 70%
x

But why do I need it? If 168.4 kg is the actual yield, and this is actually 70% of the theoretical yield, then shouldn't I just have to figure out how much profit this amount will yield?

[artwill872]

Is the theoretical amount that I'd be able to get from the equation above what I should have used to figure out the amounts of NH3 and CO2 required in the reaction?

[rabolisk]

Yes.