1 ml of H3PO4 was diluted to 250 ml 25 ml this solution required 40 CC of 0.1N -NaOH for neutralization using phenolphthalein as indicator. What is the specific gravity of acid then?

To determine the specific gravity of the phosphoric acid (H3PO4) solution, we need to follow a series of calculations based on the information provided. Let’s break this down step by step.

Understanding the Dilution and Neutralization Process

Initially, you have 1 mL of concentrated H3PO4 that is diluted to a total volume of 250 mL. This means that the concentration of the diluted solution will be significantly lower than that of the concentrated acid. The neutralization reaction involves sodium hydroxide (NaOH) reacting with phosphoric acid, and we can use the volume of NaOH required to find the moles of H3PO4 present in the diluted solution.

Step 1: Calculate Moles of NaOH Used

First, we need to find out how many moles of NaOH were used in the neutralization. The normality (N) of NaOH is given as 0.1 N, and the volume used is 40 mL (or 0.040 L). The formula to calculate moles from normality is:

• Moles = Normality × Volume (in liters)

So, the moles of NaOH used are:

Moles of NaOH = 0.1 N × 0.040 L = 0.004 moles

Step 2: Determine Moles of H3PO4

Phosphoric acid (H3PO4) is a triprotic acid, meaning it can donate three protons (H+ ions). Therefore, the neutralization reaction can be represented as:

H3PO4 + 3 NaOH → Na3PO4 + 3 H2O

This indicates that one mole of H3PO4 reacts with three moles of NaOH. To find the moles of H3PO4 that reacted, we can use the stoichiometry of the reaction:

Moles of H3PO4 = Moles of NaOH / 3 = 0.004 moles / 3 = 0.00133 moles

Step 3: Calculate the Concentration of H3PO4 in the Diluted Solution

Now that we know the moles of H3PO4 in the 25 mL of the diluted solution, we can find the concentration (in moles per liter) of H3PO4 in that solution:

Concentration of H3PO4 = Moles / Volume (in liters)

Since 25 mL is 0.025 L, we have:

Concentration of H3PO4 = 0.00133 moles / 0.025 L = 0.0532 moles/L

Step 4: Calculate the Mass of H3PO4

The molar mass of H3PO4 is approximately 98 g/mol. To find the mass of H3PO4 in the 25 mL solution, we can use the formula:

Mass = Moles × Molar Mass

Thus, the mass of H3PO4 is:

Mass = 0.00133 moles × 98 g/mol = 0.13034 g

Step 5: Determine the Specific Gravity

Specific gravity is defined as the ratio of the density of a substance to the density of a reference substance (usually water for liquids). To find the specific gravity of the H3PO4 solution, we need to know the volume of the solution and the mass we just calculated.

Since we diluted 1 mL of H3PO4 to 250 mL, we can assume that the density of the solution is close to that of water, which is 1 g/mL. Therefore, the mass of the 250 mL solution can be approximated as:

Mass of solution = Volume × Density = 250 mL × 1 g/mL = 250 g

Now, we can calculate the specific gravity:

Specific Gravity = Mass of H3PO4 / Mass of solution = 0.13034 g / 250 g = 0.00052136

Final Calculation of Specific Gravity

However, specific gravity is typically expressed in a more practical range, so we need to consider the concentration of the original acid. The specific gravity of the concentrated H3PO4 would be higher than this diluted value. To find the specific gravity of the concentrated acid, we would need to adjust our calculations based on the dilution factor and the density of concentrated H3PO4, which is around 1.88 g/mL.

Thus, the specific gravity of the concentrated H3PO4 can be approximated as:

Specific Gravity of H3PO4 = Density of H3PO4 / Density of water = 1.88 g/mL / 1 g/mL = 1.88

In summary, the specific gravity of the concentrated phosphoric acid is approximately 1.88, while the diluted solution has a much lower specific gravity due to the significant dilution. This illustrates how dilution affects the concentration and properties of solutions.