A nurse wants to add water to 18 ounces of a 10% solution of benzalkonium chloride to dilute it to an 8% solution. How much water must she add? (Hint: Water is 0% benzalkonium chloride.)
A nurse wants to add water to 22 ounces of a 10% solution of benzalkonium chloride to dilute it to an 8% solution. How much water must she add?
To solve this problem, we can use the concept of concentration and dilution. Here's how you can calculate the amount of water to be added:
Step 1: Determine the initial amount of benzalkonium chloride in the 10% solution.
In a 10% solution of 18 ounces, the amount of benzalkonium chloride is calculated as:
10% * 18 ounces = 0.10 * 18 = 1.8 ounces
Step 2: Determine the final amount of benzalkonium chloride in the 8% solution.
In an 8% solution, the amount of benzalkonium chloride should remain the same, i.e.,
1.8 ounces
Step 3: Calculate the amount of water to be added.
The difference between the initial and final amount of benzalkonium chloride should be balanced by the amount of water added, so:
18 ounces (total volume) - 1.8 ounces (final amount of benzalkonium chloride) = 16.2 ounces
Therefore, the nurse needs to add 16.2 ounces of water to dilute the 18 ounces of a 10% solution of benzalkonium chloride to an 8% solution.
To solve this problem, we can use the concept of dilution. Dilution involves adding a solvent (in this case, water) to a given solution to decrease its concentration.
Step 1: Calculate the amount of benzalkonium chloride in the original 10% solution.
The original solution is 18 ounces of a 10% solution, which means there are 10% of 18 ounces of benzalkonium chloride in it.
Amount of benzalkonium chloride = 10% of 18 ounces
= 0.10 * 18 ounces
= 1.8 ounces
Step 2: Calculate the amount of benzalkonium chloride needed in the final 8% solution.
In the final solution, we want the benzalkonium chloride concentration to be 8%, and we know that the total volume will be 18 ounces.
Amount of benzalkonium chloride needed = 8% of 18 ounces
= 0.08 * 18 ounces
= 1.44 ounces
Step 3: Calculate the amount of water to add.
To dilute the original solution, we need to add enough water to reach a total volume of 18 ounces, while also ensuring that the amount of benzalkonium chloride is reduced to 1.44 ounces.
Amount of water to add = Total volume - Amount of benzalkonium chloride needed
= 18 ounces - 1.44 ounces
= 16.56 ounces
Therefore, the nurse must add 16.56 ounces of water to the 18 ounces of the 10% solution of benzalkonium chloride to dilute it to an 8% solution.