If 3.15 mL of vinegar needs 42.5 mL of 0.115 M NaOH to reach the equivalence point in a titration, how many grams of acetic acid are in a 1.40 qt sample of this vinegar?
0.043 liters x 0.100 M = 0.0043 moles of NaOH
0.0043 moles of NaOH = 0.0043 moles of acetic acid
1 quart = 32 fl oz
1 fl oz = 29.57 mL
1.75 quarts x 32 fl oz/qt x 29.57 mL/fl oz = 1656 mL
0.0043 moles / 3.65 mL = 1.178x10^-3 moles/mL
1.178x10^-3 mol/mL x 1.656x10^3 mL = 1.95 mol
1.95 mol x 60.05 g/mol = 117 g
117 g CH3COOH per 1.75 quarts
Well, well, well, looks like we have a vinegar connoisseur in our midst! Let me entertain you with some chemistry humor while I calculate the answer for you.
Why did the scarecrow become an expert in vinegar titrations? Because he acetic-ated himself to learning everything about it!
Now, to solve the problem at hand. First, we need to convert 1.40 quarts to milliliters. Since there are approximately 946.353 mL in a quart, a 1.40-quart sample of vinegar would be roughly 1330 mL.
Now that we have that sorted, let's set up the ratio:
3.15 mL of vinegar needs 42.5 mL of 0.115 M NaOH
Using this ratio, we can determine how many milliliters of NaOH would be required for 1330 mL of vinegar. Mathematically speaking, it would look like this:
(1330 mL vinegar) / (3.15 mL vinegar) = (x mL NaOH) / (42.5 mL NaOH)
Solving for x, the number of milliliters of NaOH needed, we get:
x = (1330 mL vinegar * 42.5 mL NaOH) / (3.15 mL vinegar) ≈ 17946 mL NaOH
Now it's time to bring acetic acid into the mix! To calculate the grams of acetic acid, we need to consider the molar ratio between acetic acid and NaOH. Since the balanced equation is 1:1, the number of moles of acetic acid is equal to the number of moles of NaOH.
We can use the formula:
moles = concentration (M) * volume (L)
First, convert 17946 mL of NaOH to liters:
(17946 mL NaOH) * (1 L / 1000 mL) ≈ 17.946 L NaOH
Now, we can determine the number of moles of acetic acid:
moles acetic acid = (0.115 M NaOH) * (17.946 L NaOH) ≈ 2.064 moles acetic acid
Finally, we can calculate the grams of acetic acid using the molar mass of acetic acid, which is approximately 60.05 g/mol:
grams acetic acid = (2.064 moles acetic acid) * (60.05 g/mol) ≈ 123.988 grams acetic acid
Therefore, in a 1.40-quart sample of this vinegar, there are approximately 123.988 grams of acetic acid. Hope that puts a smile on your face, vinegar aficionado!
To solve this problem, we need to use the given information to calculate the number of moles of acetic acid in the 3.15 mL sample of vinegar. Then, we can use this information to find the number of moles of acetic acid in the 1.40 qt sample of vinegar. Finally, we can convert the moles of acetic acid to grams using the molar mass of acetic acid.
Step 1: Calculate the number of moles of acetic acid in the 3.15 mL sample of vinegar.
We know that the volume of the NaOH solution needed for neutralization is 42.5 mL, and its concentration is 0.115 M. This information allows us to calculate the number of moles of NaOH.
Number of moles of NaOH = concentration * volume
Number of moles of NaOH = 0.115 M * 0.0425 L = 0.0048875 moles
Since the equation of the reaction is 1 mol acetic acid: 1 mol NaOH, there are also 0.0048875 moles of acetic acid in the 3.15 mL sample of vinegar.
Step 2: Convert moles to grams.
The molar mass of acetic acid (CH3COOH) is approximately 60.05 g/mol.
Number of grams of acetic acid = number of moles * molar mass
Number of grams of acetic acid = 0.0048875 moles * 60.05 g/mol = 0.293 grams
So, there are approximately 0.293 grams of acetic acid in the 3.15 mL sample of vinegar.
Step 3: Calculate the number of moles of acetic acid in the 1.40 qt sample of vinegar.
1 qt is equal to 0.946352946 mL, so 1.40 qt is equal to 1.40 * 0.946352946 mL = 1.32509412 L.
Since we know the concentration of acetic acid in the vinegar sample remains the same, we can use the same concentration we calculated earlier (0.0048875 moles/L) to find the number of moles of acetic acid in the 1.32509412 L sample of vinegar.
Number of moles of acetic acid in the 1.32509412 L sample = 0.0048875 moles/L * 1.32509412 L = 0.0064741 moles
Step 4: Convert moles to grams.
Number of grams of acetic acid in the 1.40 qt sample = number of moles * molar mass
Number of grams of acetic acid in the 1.40 qt sample = 0.0064741 moles * 60.05 g/mol ≈ 0.3889 grams
Therefore, there are approximately 0.3889 grams of acetic acid in a 1.40 qt sample of this vinegar.
To find the number of grams of acetic acid in a 1.40 qt sample of vinegar, we need to follow these steps:
Step 1: Convert quarts to milliliters.
Since 1 quart is equal to 946.3529 milliliters, the volume of the vinegar sample in milliliters can be calculated as follows:
1.40 qt * 946.3529 mL/qt = 1324.49306 mL
Step 2: Determine the moles of NaOH used in the titration.
We are given that 3.15 mL of vinegar requires 42.5 mL of 0.115 M NaOH to reach the equivalence point. Using the equation M1V1 = M2V2, we can calculate the number of moles of NaOH used in the titration:
(0.115 mol/L)(42.5 mL) = (x mol/L)(3.15 mL)
42.5 * 0.115 = 3.15x
x ≈ 4.8286 mmol (millimoles) of NaOH
Step 3: Determine the number of moles of acetic acid (CH3COOH) in the vinegar sample.
From the balanced chemical equation of the reaction between acetic acid and sodium hydroxide:
CH3COOH + NaOH → CH3COONa + H2O
We can see that 1 mole of acetic acid reacts with 1 mole of NaOH.
Thus, the moles of acetic acid present in the vinegar sample is also approximately 4.8286 mmol.
Step 4: Convert moles of acetic acid to grams.
To convert moles to grams, we need to use the molar mass of acetic acid, which is 60.05 g/mol.
Using this molar mass, we can calculate the mass of acetic acid in grams:
(4.8286 mmol)(60.05 g/mol) = 289.99543 mg ≈ 0.290 g
Therefore, there are approximately 0.290 grams of acetic acid in a 1.40 qt sample of vinegar.