224 ml of dry CO2 at STP was passed in 1L NaOH sol. of unknown molarity . 10 ml of resulting sol. when titrated with 0.01 M 30 ml HCl sol. for phenolpthalein end pt. Find molarity of NaOH

1) 0.03

2) 0.04

3) 0.05

4) 0.06

To determine the molarity of the NaOH solution, we can break down the problem into a series of logical steps. First, we need to understand the reaction that occurs when carbon dioxide (CO2) is passed through sodium hydroxide (NaOH) solution. The CO2 reacts with NaOH to form sodium carbonate (Na2CO3) and sodium bicarbonate (NaHCO3). The titration with hydrochloric acid (HCl) will help us find out how much NaOH was initially present in the solution.

Step 1: Calculate Moles of CO2

At standard temperature and pressure (STP), 1 mole of any gas occupies 22.4 liters. Therefore, we can calculate the number of moles of CO2 in 224 ml:

• Convert 224 ml to liters: 224 ml = 0.224 L
• Calculate moles of CO2: moles of CO2 = volume (L) / molar volume (L/mol) moles of CO2 = 0.224 L / 22.4 L/mol = 0.01 moles

Step 2: Reaction with NaOH

The reaction between CO2 and NaOH can be represented as follows:

• CO2 + NaOH → NaHCO3 (sodium bicarbonate)
• NaHCO3 + NaOH → Na2CO3 (sodium carbonate)

From this, we can see that 1 mole of CO2 reacts with 2 moles of NaOH. Therefore, the moles of NaOH that reacted with 0.01 moles of CO2 is:

• moles of NaOH = 2 × moles of CO2 = 2 × 0.01 = 0.02 moles

Step 3: Determine Moles of NaOH in 10 ml of Solution

Since the total volume of the NaOH solution is 1 L (1000 ml), the moles of NaOH in the entire solution is 0.02 moles. Now, we need to find out how many moles of NaOH are in the 10 ml sample that was titrated:

• moles of NaOH in 10 ml = (0.02 moles / 1000 ml) × 10 ml = 0.0002 moles

Step 4: Titration with HCl

During the titration, the NaOH reacts with HCl. The balanced equation for this reaction is:

• NaOH + HCl → NaCl + H2O

From the titration, we know that 30 ml of 0.01 M HCl was used. First, we calculate the moles of HCl used:

• moles of HCl = concentration (mol/L) × volume (L) = 0.01 mol/L × 0.030 L = 0.0003 moles

Step 5: Relate Moles of NaOH to Moles of HCl

Since the reaction between NaOH and HCl is a 1:1 ratio, the moles of NaOH that reacted with the HCl is equal to the moles of HCl used:

• moles of NaOH = moles of HCl = 0.0003 moles

Step 6: Calculate Molarity of NaOH Solution

Now we can find the molarity of the NaOH solution. We know that the 10 ml sample contained 0.0003 moles of NaOH. To find the molarity (M), we use the formula:

• Molarity (M) = moles of solute / volume of solution (L)
• Volume of NaOH solution used = 10 ml = 0.010 L
• Molarity of NaOH = 0.0003 moles / 0.010 L = 0.03 M

Thus, the molarity of the NaOH solution is 0.03 M. Therefore, the correct answer is option 1) 0.03.