Question

One container of Tums® costs 4.00 dollars. Each container has eighty 1.00 g tablets. Assume each Tums® is 40.0 percent CaCO₃ by mass. Using only Tums®, you are required to neutralize 0.500 L of 0.400 M HCl. How much does this cost? Assume you are able to purchase individual tablets. Express your answer in dollars.

Answer 1

Answer:

The total cost is 1.25 dollars.

Step-by-step explanation:      

The reaction between HCl and CaCO₃ is giving by:

2HCl(aq) + CaCO₃(s)   →   CaCl₂(aq) + CO₂(g) + H₂O(l) (1)

0.500L     M: 100.01g/mol        

0.400M

According to equation (1), 2 moles of HCl react with 1 mol of CaCO₃, so to neutralize HCl, we need the next amount of CaCO₃:

$m CaCO_{3} = (\frac{1 \cdot mol HCl}{2}) \cdot M_{CaCO_{3}} = (\frac{0.500L \cdot 0.400 \frac {mol}{L}}{2}) \cdot 100.01 \frac{g}{mol} = 10.001 g$      

The CaCO₃ mass of each tablet is:

$m CaCO_{3} = 1 g_{tablet} \cdot \frac{40g CaCO_{3}}{100g_{tablet}} = 0.4g$

Hence, the number of tablets that we need to neutralize the HCl is:

$number_{tablets} = ( \frac{1 tablet}{0.4 g CaCO_{3}}) \cdot 10.001g CaCO_{3} = 25$  

Finally, if every 80 tablets costs 4.00 dollars, 25 tablets will cost:

$cost = (\frac {4 dollars}{80 tablets}) \cdot 25 tablets = 1.25 dollars$

So, the total cost to neutralize the HCl is 1.25 dollars.

I hope it helps you!