Determine the molar mass of the unknown acid.?

A 0.167-g sample of an unknown acid requires 27.8 mL of 0.100 M NaOH to titrate to the equivalence point. Elemental analysis of the acid gives the following percentages by mass: 40.00% C; 6.71% H; 53.29% O.

And the question is?

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To determine the molar mass of the unknown acid, we can use the information provided and perform the following steps:

Step 1: Convert the mass of the acid sample to moles.
Given: Mass of the acid sample = 0.167 g

Molar mass (Molar mass = Mass / Moles)
Moles of the acid sample = Mass / Molar mass

Step 2: Calculate the number of moles of NaOH used during titration.
Given: Volume of NaOH used = 27.8 mL = 0.0278 L
Given: Concentration of NaOH = 0.100 M

Moles of NaOH used = Concentration of NaOH x Volume of NaOH used

Step 3: Set up the balanced equation for the reaction between the acid and NaOH.
The balanced equation for the reaction between the acid and NaOH can be written as follows:

Acid + NaOH -> Salt + H2O

Since we're only interested in the molar ratios, we can assume a simplified balanced equation like this:
1 mol Acid = 1 mol NaOH

Step 4: Determine the moles of the acid using the moles of NaOH.
Since the moles of acid and NaOH are equal according to the balanced equation, the moles of the acid can be calculated as follows:

Moles of Acid = Moles of NaOH

Step 5: Use the percent composition to determine the empirical formula of the acid.
Given: Percentage of Carbon (C) = 40.00%
Given: Percentage of Hydrogen (H) = 6.71%
Given: Percentage of Oxygen (O) = 53.29%

Assuming a 100 g sample, we can determine that:
Mass of carbon (C) = 40.00 g
Mass of hydrogen (H) = 6.71 g
Mass of oxygen (O) = 53.29 g

To convert the masses to moles, we divide by the respective atomic masses:
Moles of C = Mass of C / Molar mass of C = 40.00 g / 12.01 g/mol
Moles of H = Mass of H / Molar mass of H = 6.71 g / 1.01 g/mol
Moles of O = Mass of O / Molar mass of O = 53.29 g / 16.00 g/mol

Step 6: Determine the ratios of the elements and find the empirical formula of the acid.
The ratio of the elements can be determined by dividing each number of moles by the smallest number of moles:

C: (Moles of C) / (Smallest number of moles)
H: (Moles of H) / (Smallest number of moles)
O: (Moles of O) / (Smallest number of moles)

Step 7: Determine the empirical formula mass of the acid.
The empirical formula mass is the sum of the atomic masses of the empirical formula. Multiply the atomic masses by the respective subscripts obtained from the previous step:

Empirical formula mass = (Atomic mass of C) x (Number of C atoms) + (Atomic mass of H) x (Number of H atoms) + (Atomic mass of O) x (Number of O atoms)

Step 8: Determine the molecular formula mass of the acid.
The molecular formula mass is the actual molar mass of the acid, which is what we're trying to find. If given, we can divide the molecular formula mass by the empirical formula mass to determine the ratio of the two:

Molecular formula mass / Empirical formula mass = n (an integer)

Step 9: Determine the molar mass of the acid.
Multiply the empirical formula mass by the integer obtained in the previous step:

Molar mass of the acid = Empirical formula mass x n

By following these steps, you should be able to determine the molar mass of the unknown acid.

To determine the molar mass of the unknown acid, we need to follow a step-by-step approach:

Step 1: Calculate the number of moles of NaOH used in the titration.
We know the volume (27.8 mL) and concentration (0.100 M) of NaOH used. The equation for the reaction between the acid and NaOH is:

Acid + NaOH → Salt + Water

Since the acid and NaOH react in a 1:1 ratio, the number of moles of NaOH used is given by:

moles of NaOH = volume (in L) × concentration (in mol/L)

Convert the volume from milliliters (mL) to liters (L):

27.8 mL = 27.8 × 10^(-3) L

Calculate the moles of NaOH:

moles of NaOH = 27.8 × 10^(-3) L × 0.100 mol/L

Step 2: Convert the mass percentage of each element to moles.
The percentages of C, H, and O present in the acid are given. We can assume a 100 g sample of the acid, making the mass percentages equal to grams of each element in the acid.

Calculate the masses of C, H, and O in the 100 g sample:

Mass of C = 40.00 g (40.00% of 100 g)
Mass of H = 6.71 g (6.71% of 100 g)
Mass of O = 53.29 g (53.29% of 100 g)

Convert the masses of each element to moles using their respective molar masses:

moles of C = Mass of C / Molar mass of C
moles of H = Mass of H / Molar mass of H
moles of O = Mass of O / Molar mass of O

Step 3: Determine the empirical formula of the acid.
The empirical formula represents the simplest ratio of atoms in a compound. To find it, we divide the number of moles of each element by the smallest number of moles obtained in step 2.

Divide the moles of each element by the smallest number of moles:

C: moles of C / smallest number of moles
H: moles of H / smallest number of moles
O: moles of O / smallest number of moles

Step 4: Determine the molar ratio of the elements.
Now that we have the empirical formula, we need to find the ratio of atoms in the compound to determine the molar mass. We can use the molar mass of each element to calculate the total molar mass.

Multiply each atom's molar mass by its corresponding subscript in the empirical formula:

Molar mass of C = molar mass of C × coefficient in the empirical formula
Molar mass of H = molar mass of H × coefficient in the empirical formula
Molar mass of O = molar mass of O × coefficient in the empirical formula

Add up the molar masses of each element to get the molar mass of the unknown acid:

Molar mass of the unknown acid = sum of the molar masses of C, H, and O

Following these steps, you can determine the molar mass of the unknown acid.