Here's the problem: You need to make 300L of 2.25M perchloric acid. It costs $25.95 for a 4.00 liter bottle of 60% HClO4, and $34.95 for a 4.00 liter bottle of 70% HClO4. Should you buy the 60% or the 70% bottles? Show your calculations and explain.
To determine which option is more cost-effective, we need to compare the cost per liter of perchloric acid for each bottle.
Let's start by calculating the moles of HClO4 we need in order to make 300L of 2.25M perchloric acid:
moles of HClO4 = volume of perchloric acid (L) * concentration of perchloric acid (M)
= 300 L * 2.25 M
= 675 moles of HClO4
Now, let's find the number of moles of HClO4 in each bottle. We can use the given concentration and volume to calculate this:
moles of HClO4 in a 4L bottle = volume of bottle (L) * concentration of HClO4 (M)
For the 60% bottle:
moles of HClO4 in a 4L bottle of 60% HClO4 = 4 L * 0.60 M
= 2.40 moles of HClO4
For the 70% bottle:
moles of HClO4 in a 4L bottle of 70% HClO4 = 4 L * 0.70 M
= 2.80 moles of HClO4
Now, let's calculate the cost per mole of HClO4 for each bottle:
Cost per mole of HClO4 for the 60% bottle = cost of bottle / moles of HClO4 in a 4L bottle of 60% HClO4
= $25.95 / 2.40 moles of HClO4
= $10.81/mole of HClO4
Cost per mole of HClO4 for the 70% bottle = cost of bottle / moles of HClO4 in a 4L bottle of 70% HClO4
= $34.95 / 2.80 moles of HClO4
= $12.48/mole of HClO4
Finally, we compare the cost per mole of HClO4 for each bottle. The lower cost per mole indicates the more cost-effective option:
Cost per mole of HClO4:
- 60% bottle: $10.81/mole of HClO4
- 70% bottle: $12.48/mole of HClO4
Since the 60% bottle has a lower cost per mole of HClO4, it is the more cost-effective option. Therefore, you should buy the 60% bottle to make 300L of 2.25M perchloric acid.