A student performs a back-titration to determine the cost -effectiveness of an antacid. A tablet with a retail cost of $0.053 is dissolved in 25.00 ml of 1.000 M HCl, then back-titrated with 1.000 M NaOH. Exactly 14.82 ml of NaOH solution is required to reach the endpoint. Express the volume of HCl solution in liters.
moles HCl initially = M x L.
moles NaOH = M x L
moles NaOH = moles HCl in excess.
moles HCl initial - mols HCl excess = moles used by actacid.
I'm confused by "express the volum of HCl solution in liters" but the information is above. If the answer is to be expressed in liters, then I would suggest molarity = moles/L and rearrange to
L - moles/M = moles used/M
To find the volume of the HCl solution in liters, we start by converting the given volume of the NaOH solution used to reach the endpoint from milliliters to liters.
Given:
Volume of NaOH solution used = 14.82 mL
To convert mL to L, we divide the volume by 1000:
Volume of NaOH solution used = 14.82 mL ÷ 1000 = 0.01482 L (rounded to 5 decimal places)
Now we know the volume of the NaOH solution used in liters. In a back-titration, the moles of the analyte (HCl in this case) can be determined from the moles of the back-titrant (NaOH). The ratio of moles between the analyte and back-titrant can be used to calculate the volume of the analyte.
From the balanced equation for the reaction between HCl and NaOH:
HCl + NaOH → NaCl + H2O
We can see that 1 mole of HCl reacts with 1 mole of NaOH. Therefore, the moles of HCl can be calculated using the volume and concentration of NaOH.
Given:
Volume of NaOH solution used = 0.01482 L
Concentration of NaOH solution = 1.000 M (Molarity)
Using the formula:
moles = concentration × volume
moles of NaOH = 1.000 M × 0.01482 L = 0.01482 moles
Since the ratio of moles between HCl and NaOH is 1:1, the moles of HCl are also 0.01482 moles.
Finally, to calculate the volume of the HCl solution in liters, we divide the number of moles of HCl by its concentration.
Given:
Molarity of HCl solution = 1.000 M
Using the formula:
moles = concentration × volume
0.01482 moles = 1.000 M × volume of HCl solution
volume of HCl solution = 0.01482 moles ÷ 1.000 M = 0.01482 L
Therefore, the volume of the HCl solution is 0.01482 liters.