A 0.125-g sample of monoprotic acid of unknown molar mass is dissolved in water and titrated with 0.1003 M NaOH. The endpoint is reached after adding 20.77 mL of base. What is the molar mass of the unknown acid?

To find the molar mass of the unknown acid, we need to calculate the number of moles of the acid and divide it by the mass of the acid.

First, we need to find the number of moles of NaOH that reacted with the acid.

Since the concentration of NaOH is 0.1003 M and the volume of NaOH used is 20.77 mL (or 0.02077 L), we can calculate the number of moles of NaOH as follows:

Number of moles of NaOH = Concentration of NaOH × Volume of NaOH
= 0.1003 M × 0.02077 L
≈ 0.002080 mol

Since NaOH reacts with the acid in a 1:1 molar ratio, the number of moles of the unknown acid is also approximately 0.002080 mol.

Next, we need to find the mass of the acid. Given that the mass of the acid is 0.125 g, we can calculate the molar mass of the unknown acid as follows:

Molar mass of the unknown acid = Mass of the acid / Number of moles of the acid
= 0.125 g / 0.002080 mol
≈ 60.10 g/mol

Therefore, the molar mass of the unknown acid is approximately 60.10 g/mol.

To find the molar mass of the unknown acid, we need to use the concept of titration and stoichiometry. Here is how you can solve the problem step by step:

1. Convert the given mass of the sample to moles of the acid.
- The mass of the sample given is 0.125 g.

molar mass (M) = mass (m) / moles (n)
n = m / M

Let's assume M as the molar mass of the unknown acid.
n = 0.125 g / M g/mol

2. Determine the moles of NaOH used in the titration.
- The volume of NaOH used is 20.77 mL, which is equivalent to 0.02077 L.
- The concentration of NaOH is 0.1003 M.

moles of NaOH (nNaOH) = concentration (C) × volume (V)
nNaOH = 0.1003 M × 0.02077 L

3. Use the balanced chemical equation to relate moles of unknown acid to moles of NaOH.
- The balanced equation for the acid-base reaction will provide the stoichiometric relationship between the unknown acid and NaOH.

Assuming the equation is: Acid + NaOH → Salt + Water
The balanced stoichiometric coefficients (from the equation) will give us the ratio of moles between the unknown acid and NaOH.

Let's say the stoichiometric coefficient of the unknown acid is x: Acid + x NaOH → Salt + Water

From the balanced equation, we can conclude that:
x moles of NaOH react with 1 mole of the unknown acid.

4. Set up an equation using the known information to calculate the molar mass of the unknown acid.
- From steps 2 and 3, we have the moles of the acid (n) and the moles of NaOH used (nNaOH) in the reaction.

nNaOH = x moles of unknown acid

Solving for x:
x = nNaOH

Substitute the value of x in terms of moles of NaOH used:
0.1003 M × 0.02077 L = n / M

Rearrange the equation to solve for M:
M = n / (0.1003 M × 0.02077 L)

Substitute the value of n from step 1:
M = (0.125 g / M g/mol) / (0.1003 M × 0.02077 L)

5. Solve for M (molar mass):

Let's calculate the molar mass:

M ≈ 0.125 g / (0.1003 M × 0.02077 L)

Using a calculator, the approximate value of M is:
M ≈ 600 g/mol

Therefore, the molar mass of the unknown acid is approximately 600 g/mol.

Balance the reaction first, then procede as you did in the other. Monoprotic means Hx

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