Solve each of the following problems:
d. A bottle containing 325 g of cleaning solution is used to clean hospital equipment. If the cleaning solution has a specific gravity of 0.850, what volume, in milliliters, of solution was used?

Question

Solve each of the following problems:

d. A bottle containing 325 g of cleaning solution is used to clean hospital equipment. If the cleaning solution has a specific gravity of 0.850, what volume, in milliliters, of solution was used?

Accepted Answer

Welcome back everyone. One of the uses of vinegar is being an ingredient for insect repellent. An insect repellent was made using 385 g of vinegar. If the specific gravity of vinegar is one point oh one, determine the volume in milliliters of vinegar yeast. So let's begin by recalling that our formula to calculate specific gravity of a substance can be found by taking our density of our substance. So density recall is expressed by roe and then this will be divided by our density of water. And specifically, we're going to be considering the density of water at 4°C. And we're utilizing the temperature of 4°C because we want to recall that our density of water at four degrees Celsius will be at its maximum being at one point oh grams per milliliter of four degrees Celsius. So now with this formula outlined, we're given our specific gravity of vinegar as one point oh one. However, we're not, we're going to need to find the volume in milliliters of vinegar. So we're going to need our density of vinegar and we can just rearrange our specific gravity formula to isolate for density of our substance in which we want to multiply both sides by the density of water so that it will cancel out on the right. And then we will have our specific gravity. I'll use S P G as shorthand for that times our density of water equal to the density of our substance in this case, vinegar. And so in order to find our density of vinegar, we're going to take its given specific gravity from the prompt being 1.01. And then we're going to multiply by the density of water which we know at 4°C. As we noted above is 1.0 g per milliliter. And so from this calculation, we'll find our density of vinegar equal to one point oh one g per milliliter. Now, with our density of vinegar, as we stated before, we need to find the volume of vinegar. And we're going to recall that density is equal to mass over volume row is equal to mass over volume. So we can isolate for volume by multiplying both sides by V so that it can cancel it on the right. And we have in our next line road times volume equal to mass. And now dividing both sides by row so that it cancels out on the left, we'll find that volume is equal to mass over density. So now with this formula outlined, let's get into calculating again the volume of our vinegar. So this is going to be again, set equal to our mass of vinegar divided by our density of vinegar. So, plugging in our terms for our numerator, for the mass of vinegar from our prompt above, we're given a mass of 358 g of vinegar. And then in our denominator, our density of vinegar, which we just calculated is one point oh one g per milliliter. So canceling out our units of grams. We're left with units of milliliters as our unit of volume. And in our calculators, we're going to find that our volume of vinegar is equal to the value 354 mL. And so 354 ml will be our final answer as our volume of vinegar given its specific gravity as 1.01. So I hope that this made sense and let us know if you have any questions.

Solve each of the following problems:
d. A bottle containing 325 g of cleaning solution is used to clean hospital equipment. If the cleaning solution has a specific gravity of 0.850, what volume, in milliliters, of solution was used?

Verified video answer for a similar problem:

Key Concepts

Specific Gravity

Density

Volume Calculation

Solve each of the following problems:d. A bottle containing 325 g of cleaning solution is used to clean hospital equipment. If the cleaning solution has a specific gravity of 0.850, what volume, in milliliters, of solution was used?

Verified video answer for a similar problem:

Key Concepts

Specific Gravity

Density

Volume Calculation

Solve each of the following problems:
d. A bottle containing 325 g of cleaning solution is used to clean hospital equipment. If the cleaning solution has a specific gravity of 0.850, what volume, in milliliters, of solution was used?