I may need this broken down step by step to understand this problem thanks. A 20.0% by mass solution of phosphoric acid (H3PO4) in water has a density of 1.114 g/ml at 20℃. What is the molarity of the solution?

I could just give you a formula that will do this; I memorized it years ago but here is a question by question approach.

What is the definition of molarity.
M = mols/L. So that's what we need to determine.
How much does a L weigh? That's
1.114 g/mL x 1000 mL = 1114 grams. Simple enough, eh?
How much of that 1114 g is H3PO4. It says it is 20% by mass, therefore, 1114 g x 0.20 = 222.8 g.
How many mols are there in 222.8 g H3PO4? That's mools = grams/molar mass = 222.8/98 = 2.273 mols.
The definition of M is what? M = mols/L. And you have 2.273 mol/L; that must be the molarity.

The formula is
density g/mL x 1000 mL x mass% x (1/molar mass) = M
1.114 x 1000 x 0.20 x (1/98) = 2.273 M.
Have a good day.

a liter of solution has a mass of 1.114 kg

20.0% of that is H₃PO₄ ... 222.8 g

the molar mass of H₃PO₄ is ... 97.99 g

so the moles/L is ... 222.8 / 97.99

the 20.0 means 3 sig fig

Step 1: Identify the given information:

- The solution has a concentration of phosphoric acid of 20.0% by mass.
- The density of the solution is 1.114 g/ml at 20℃.

Step 2: Convert the mass percentage to grams:
Since the solution is 20.0% by mass, it means that for every 100 grams of solution, 20 grams are phosphoric acid. So if we have "x" grams of the solution, we have 20% of that as phosphoric acid, which can be written as 0.2x grams.

Step 3: Determine the volume of the solution:
We are given the density of the solution, which is 1.114 g/ml. The density is defined as mass/volume, so we can rearrange the equation to find the volume:
Volume = mass/density
Since we already know the mass of the solution (x grams), we can substitute it into the equation:
Volume = x/1.114

Step 4: Calculate the molarity:
Molarity (M) is defined as moles of solute per liter of solution. To find the molarity of the phosphoric acid solution, we first need to find the moles of phosphoric acid present. We can use the equation:
moles = mass/molar mass
The molar mass of phosphoric acid (H3PO4) can be calculated by adding up the atomic masses of each element:
(3 x atomic mass of hydrogen) + (1 x atomic mass of phosphorus) + (4 x atomic mass of oxygen)

Step 5: Convert grams of phosphoric acid to moles:
Using the moles = mass/molar mass equation, we can convert the mass of phosphoric acid from grams to moles. The mass of phosphoric acid is 0.2x grams, as calculated in step 2.

Step 6: Calculate the volume in liters:
Since molarity is moles per liter, we need to convert the volume of the solution from milliliters to liters. The volume was calculated in step 3.

Step 7: Plug the values into the molarity formula:
Molarity = moles/volume

Step 8: Simplify the molarity:
Calculate the final value for the molarity, which is moles per liter.

Step 9: Round the final answer:
Round the molarity value to an appropriate number of significant figures, usually based on the given information or the desired level of precision.

By following these step-by-step instructions, you should be able to find the molarity of the given solution of phosphoric acid.

To find the molarity of a solution, we need to know the mass of solute (in this case, phosphoric acid) and the volume of solution. Here are the step-by-step breakdown to solve the problem:

Step 1: Calculate the mass of phosphoric acid:
- We are given that the solution is 20.0% by mass, which means that for every 100 grams of the solution, 20 grams of it is phosphoric acid.
- Let's assume we have 100 grams of the solution. Therefore, the mass of phosphoric acid in this 100-gram solution is 20 grams.

Step 2: Calculate the volume of the solution:
- We are given that the density of the solution is 1.114 g/ml at 20°C. Density is defined as mass divided by volume: density = mass/volume.
- Rearranging the formula, we can calculate the volume: volume = mass/density.
- In our case, the mass of the solution is 100 grams (as assumed in step 1) and the density is 1.114 g/ml. Therefore, the volume of the solution is 100 g / 1.114 g/ml = 89.76 ml.

Step 3: Convert the volume of the solution to liters:
- Since molarity is defined as moles of solute per liter of solution, we need to convert the volume of the solution from milliliters (ml) to liters (L).
- There are 1000 milliliters in a liter, so the volume of the solution in liters is 89.76 ml / 1000 = 0.08976 L.

Step 4: Calculate the molarity:
- Molarity (M) is defined as moles of solute per liter of solution. Since we have already calculated the mass of phosphoric acid in step 1, we can now calculate the moles of phosphoric acid.
- The molar mass of phosphoric acid (H3PO4) can be calculated as follows:
- 3 atoms of hydrogen (H) with an atomic mass of 1 g/mol each: 3 g/mol
- 1 atom of phosphorus (P) with an atomic mass of 31 g/mol: 31 g/mol
- 4 atoms of oxygen (O) with an atomic mass of 16 g/mol each: 64 g/mol
- The molar mass of H3PO4 = 3x1 + 1x31 + 4x16 = 98 g/mol.
- Now, we can calculate the moles of phosphoric acid: moles = mass / molar mass.
- In our case, the mass of phosphoric acid as calculated in step 1 is 20 grams. Therefore, moles of phosphoric acid = 20 g / 98 g/mol = 0.204 mol.

- Finally, we divide the moles of solute (0.204 mol) by the volume of solution in liters (0.08976 L) to get the molarity:
- Molarity = moles of solute / volume of solution
- Molarity = 0.204 mol / 0.08976 L ≈ 2.273 M

Therefore, the molarity of the 20.0% by mass solution of phosphoric acid in water is approximately 2.273 M.