Concentrated phosphoric acid is 90% by mass and the remaining mass is water.The molarity of phosphoric acid in 90% is 12.2M at rtp.
a)What is the density of the solution at rtp ?
b)What volume (in mL)of this solution is needed to make a 1.00L solution of a 1.00M phosphoric acid ?
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To solve this problem, we can use the definition of molarity and the relationship between mass, volume, and density.
a) To find the density of the solution at room temperature and pressure (rtp), we need to know the density of pure water and the density of 90% phosphoric acid solution. The density of pure water at rtp is approximately 1.00 g/mL.
To find the density of the 90% phosphoric acid solution, we need to calculate the total mass of the solution. Since the solution is 90% phosphoric acid and the remaining mass is water, we can assume that the total mass is equal to the mass of the 90% phosphoric acid.
Let's assume that we have 100 g of the solution. Since it is 90% phosphoric acid by mass, the mass of the phosphoric acid is 90 g. Therefore, the mass of water is 100 g - 90 g = 10 g.
Now, we can calculate the volume of the solution using the formula:
Volume (mL) = Mass (g) / Density (g/mL)
For the 90% phosphoric acid solution:
Volume = 100 g / Density
For the pure water:
Volume = 10 g / 1 g/mL = 10 mL
Since the total volume is the sum of the volumes of phosphoric acid and water, we have:
Volume (solution) = Volume (phosphoric acid) + Volume (water)
Volume (solution) = 100 mL + 10 mL
Volume (solution) = 110 mL
Now we can calculate the density of the solution:
Density = Mass (solution) / Volume (solution)
Density = 100 g / 110 mL
Density ≈ 0.909 g/mL
Therefore, the density of the 90% phosphoric acid solution at rtp is approximately 0.909 g/mL.
b) To find the volume of the 90% phosphoric acid solution needed to make a 1.00 L solution of 1.00 M phosphoric acid, we can use the formula:
Molarity (M) = Moles (mol) / Volume (L)
We know that the molarity of the 90% phosphoric acid solution is 12.2 M, so:
12.2 M = Moles / 0.1 L (since we have 100 mL of the solution, which is equal to 0.1 L)
Rearranging the formula to solve for moles:
Moles = Molarity * Volume
Moles = 12.2 M * 0.1 L = 1.22 moles
Now, we can use the stoichiometry of the phosphoric acid (H3PO4) to calculate the volume of the 90% phosphoric acid solution needed.
From the balanced chemical equation, we know that one mole of H3PO4 is equivalent to three moles of H+ ions. Therefore, the number of moles of phosphoric acid (H3PO4) is the same as the number of moles of H+ ions.
Since we want a 1.00 M solution of phosphoric acid, we need 1.22 moles of H3PO4.
1.22 moles H3PO4 * (1 L / 1 M) = 1.22 L
Therefore, we need 1.22 L of the 90% phosphoric acid solution to make a 1.00 L solution of 1.00 M phosphoric acid. Converting this to mL:
Volume = 1.22 L * 1000 mL/L = 1220 mL
Therefore, we need 1220 mL of the 90% phosphoric acid solution.
To find the density of the solution, we need to know the mass and volume of the solution. The mass of the solution can be calculated by considering the mass percentage of phosphoric acid.
a) Finding the density of the solution:
We are given that the concentrated phosphoric acid is 90% by mass. Therefore, if we assume the total mass of the solution to be 100 g, 90 g will be phosphoric acid and the remaining 10 g will be water.
Density (ρ) is defined as the mass (m) divided by the volume (V):
ρ = m/V
Now, let's find the mass of the solution:
mass of the solution = mass of phosphoric acid + mass of water
mass of the solution = 90 g + 10 g
mass of the solution = 100 g
The volume of the solution is not provided, so we cannot calculate the density with this information. Density depends on both mass and volume. To find the density, the volume information is needed.
b) Finding the volume of concentrated phosphoric acid needed to make a 1.00 L solution of 1.00 M phosphoric acid:
The molarity of the phosphoric acid in the 90% solution is given as 12.2 M. Molarity (M) is defined as the number of moles (n) of solute divided by the volume (V) of the solution in liters:
M = n/V
We can rearrange the equation to solve for the volume (V):
V = n/M
Now, we need to find the number of moles of phosphoric acid. To do this, we need to know the molar mass of phosphoric acid. The molar mass of phosphoric acid (H₃PO₄) is:
(3 × atomic mass of hydrogen) + atomic mass of phosphorus + (4 × atomic mass of oxygen)
= (3 × 1.008) + 30.97 + (4 × 15.999)
= 97.995 g/mol
To find the moles of acid, we use the formula:
moles of phosphoric acid = mass of phosphoric acid / molar mass of phosphoric acid
moles of phosphoric acid = 90 g / 97.995 g/mol
moles of phosphoric acid = 0.918 mol
Now, we can calculate the volume of the concentrated phosphoric acid needed:
V = 0.918 mol / 12.2 M
V = 0.075 L
To convert liters to milliliters, we multiply by 1000:
V = 0.075 L × 1000 mL/L
V = 75 mL
Therefore, 75 mL of the concentrated phosphoric acid solution is needed to make a 1.00 L solution of 1.00 M phosphoric acid.