Given the following acid base titration reaction equation

Question

HCl + NaOH to produce NaCl + H2O
HCl has a concentration of 0.099875M and volume of 10.5mL, NaOH has a concentration of 0.052434375M and volume of 20mL. Calculate the concentration of NaCl in part per million.

Answer 1

To find the concentration of NaCl in parts per million (ppm) after the titration of HCl with NaOH, we'll first need to determine the number of moles of HCl and NaOH involved in the reaction and then calculate the mass of NaCl produced, followed by the concentration in ppm.

Step 1: Calculate Moles of HCl and NaOH

1. Calculate moles of HCl: \[ \text{Moles of HCl} = \text{Concentration (M)} \times \text{Volume (L)} \] Here, the volume of HCl needs to be converted to liters: \[ 10.5 \text{ mL} = 0.0105 \text{ L} \] \[ \text{Moles of HCl} = 0.099875 , \text{M} \times 0.0105 , \text{L} = 0.0010486875 \text{ moles} \]

2. Calculate moles of NaOH: \[ \text{Moles of NaOH} = \text{Concentration (M)} \times \text{Volume (L)} \] Again, convert the volume of NaOH to liters: \[ 20 \text{ mL} = 0.020 \text{ L} \] \[ \text{Moles of NaOH} = 0.052434375 , \text{M} \times 0.020 , \text{L} = 0.0010486875 \text{ moles} \]

Step 2: Determine Limiting Reactant and Product Formation

From the balanced equation \( \text{HCl} + \text{NaOH} \rightarrow \text{NaCl} + \text{H}_2\text{O} \), it's clear that HCl and NaOH react in a 1:1 ratio. Since we calculated that both HCl and NaOH produce equivalent moles, neither is limiting; they completely react with each other.

Step 3: Calculate Moles of NaCl Produced

Since the reaction stoichiometry is 1:1, the moles of NaCl produced will be equal to the moles of HCl (or NaOH): \[ \text{Moles of NaCl} = 0.0010486875 \text{ moles} \]

Step 4: Calculate Mass of NaCl

Using the molar mass of NaCl (approximately 58.44 g/mol): \[ \text{Mass of NaCl} = \text{Moles} \times \text{Molar Mass} = 0.0010486875 \times 58.44 , \text{g/mol} \approx 0.06124 , \text{g} \]

Step 5: Calculate Concentration of NaCl in ppm

To find concentration in ppm, we first need to know the total volume of the solution after mixing HCl and NaOH. The total volume (in liters) is \(0.0105 + 0.020 = 0.0305 \text{ L}\).

Next, the concentration in ppm is calculated as: \[ \text{ppm} = \left(\frac{\text{mass of solute (g)}}{\text{total volume (L)}}\right) \times 1000 , \text{(for mg/L)} \]

Converting the total volume in liters to milliliters: \[ \text{Total volume} = 30.5 \text{ mL} \]

The mass in mg is: \[ 0.06124 , \text{g} = 61.24 , \text{mg} \]

Therefore: \[ \text{ppm} = \left(\frac{61.24 , \text{mg}}{30.5 , \text{mL}}\right) \times 1000 \approx 2007.54 , \text{ppm} \]

Final Answer

The concentration of NaCl in the solution after the titration is approximately 2007.54 ppm.