if one had one gallon of sodium hydroxide solution which had a concentration of four gallons of the acid?

You need to rewrite this. As is it makes no sense.

if one had one gallon of sodium hydroxide solution which had a concentration of two pounds of sodium hydroxide per gallon.what would be the concentration of four gallons of the acid?

It still doesn't make sense. You give concns of NaOH and ask a question about acid. If this is a lab exercise, you need to give enough information for us to know what is going on.

On another note, you need to start showing us some work. My freebie help is about to run out of steam.

To solve this problem, we need to understand the concept of concentration in chemistry. Concentration refers to the amount of solute (in this case, sodium hydroxide) dissolved in a given amount of solvent (in this case, water).

In this question, it states that the concentration of the sodium hydroxide solution is four gallons of the acid. However, it is important to note that concentration is usually expressed as a ratio of the solute to the solvent, rather than as a volume.

To help us solve this problem, we need to have the concentration expressed in the appropriate unit. Let's assume that the concentration is four moles of sodium hydroxide for every one liter (or gallon) of water. In this case, we can proceed to find the amount of sodium hydroxide in one gallon of solution.

To determine the amount of sodium hydroxide, we need the molar mass of sodium hydroxide, which is 40 grams per mole for NaOH. Therefore, four moles of NaOH would weigh 4 * 40 = 160 grams.

Now, let's convert the weight to gallons. Assuming the density of the solution to be 1g/mL and considering that there are approximately 3.8 liters in a gallon, the weight of 160 grams will be equal to 160 mL or 0.16 liters.

So, in summary, if you have one gallon of sodium hydroxide solution with a concentration of four gallons of the acid, it would contain approximately 0.16 liters (or 160 mL) of sodium hydroxide.