0.2 g of a metal (atomic wt=51)liberates 87.8 ml of H₂ gas at S.T.P by reacttion with dil.H₂SO₄ .the resulting solution has reducing properties and consumed 58.8 ml of 0.2N KMnO4.calculate valencies

To determine the valency of the metal based on the information provided, we need to analyze the chemical reactions and the stoichiometry involved. The metal reacts with dilute sulfuric acid (H2SO4) to liberate hydrogen gas (H2), and the resulting solution has reducing properties, which suggests that the metal is likely undergoing oxidation. The consumption of potassium permanganate (KMnO4) in a redox reaction further indicates the metal's valency. Let's break this down step by step.

Step 1: Calculate Moles of Hydrogen Gas Produced

At standard temperature and pressure (S.T.P), 1 mole of any gas occupies 22.4 liters (or 22,400 mL). Given that 87.8 mL of H2 gas is produced, we can calculate the number of moles of H2:

• Volume of H2 = 87.8 mL = 0.0878 L
• Moles of H2 = Volume / Molar Volume = 0.0878 L / 22.4 L/mol = 0.00392 moles

Step 2: Relate Moles of Metal to Moles of Hydrogen

The reaction between the metal (M) and sulfuric acid can be represented as:

M + H2SO4 → MSO4 + H2

From the reaction, we can see that 1 mole of metal liberates 1 mole of hydrogen gas. Therefore, the moles of metal that reacted can be directly related to the moles of hydrogen produced:

• Moles of metal = Moles of H2 = 0.00392 moles

Step 3: Calculate the Equivalent Weight of the Metal

The equivalent weight of a substance is calculated using the formula:

Equivalent Weight = Atomic Weight / Valency

We know the atomic weight of the metal is 51 g/mol. To find the valency, we first need to calculate the equivalent weight based on the amount of metal used:

• Mass of metal = 0.2 g
• Equivalent weight = Mass / Moles = 0.2 g / 0.00392 moles = 51.02 g/mol

Step 4: Determine the Valency

Now, we can rearrange the equivalent weight formula to find the valency:

• Valency = Atomic Weight / Equivalent Weight
• Valency = 51 g/mol / 51.02 g/mol ≈ 1

Step 5: Analyze the Reaction with KMnO4

The solution consumed 58.8 mL of 0.2N KMnO4. To find out how many equivalents of KMnO4 were used, we can use the formula:

• Normality (N) = Equivalents / Volume (L)
• Equivalents of KMnO4 = Normality × Volume = 0.2 eq/L × 0.0588 L = 0.01176 equivalents

Since KMnO4 acts as an oxidizing agent, the equivalents of the metal that reacted can be inferred from the equivalents of KMnO4 consumed. This further supports the valency we calculated earlier.

Final Thoughts

In summary, the valency of the metal is approximately 1, which indicates that it can lose one electron during the reaction. This aligns with its behavior as a reducing agent in the presence of KMnO4. Understanding these relationships helps in grasping the fundamental concepts of redox reactions and stoichiometry in chemistry.