Question

einswine has been playing in the mud and really needs a bath. how much soap does he need to make a 2% soap solution in a 100-gallon tub? assume that the density of soap is the same as the density of water

Answer 1

To make a 2% soap solution in a 100-gallon tub, 7570.82 g (approximately 8 kg) of soap is required, assuming the density of soap is equal to water.

Step-by-step explanation:

The question is about calculating the amount of soap needed to make a 2% soap solution in a 100-gallon tub. Assuming the density of soap is the same as water, which is approximately 1000 g/L, we can calculate the necessary soap mass. Since 1 gallon is approximately 3.78541 L, a 100-gallon tub would contain about 378.541 L of water.

First, convert the volume of water into grams knowing that 1 L of water is equivalent to 1000 g:

• 378.541 L × 1000 g/L = 378541 g

Next, determine the mass of soap needed to create a 2% solution:

• 2% of 378541 g = 0.02 × 378541 g = 7570.82 g

Therefore, the mass of soap required is 7570.82 g, which is equivalent to 7.57082 kg or approximately 8 kg when rounded for practical purposes. It's important to note that this calculation assumes that no volume change occurs when soap is dissolved in water.