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

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

The CaCO₃ mass of each tablet is:

`m CaCO_(3) = 1 g_(tablet) \cdot (40g CaCO_(3))/(100g_(tablet)) = 0.4g`

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

`number_(tablets) = ( (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!