Question

In acidic medium, dichromate ion oxidize ferrous ion to ferric ion. If the gram molecular weight of potassium dichromate is \(294 \mathrm{~g}\), its equivalent weight is (a) 19 (b) 49 (c) 99 (d) 294

Short answer

The equivalent weight of potassium dichromate is 49 g/equivalent.

Step-by-step solution

Understand the Reaction

The dichromate ion ( ext{Cr}_2 ext{O}_7^{2-}) is used to oxidize ferrous ion ( ext{Fe}^{2+}) to ferric ion ( ext{Fe}^{3+}) in an acidic medium. The balanced redox reaction is: \[ ext{Cr}_2 ext{O}_7^{2-} + 14 ext{H}^+ + 6 ext{Fe}^{2+} ightarrow 2 ext{Cr}^{3+} + 7 ext{H}_2 ext{O} + 6 ext{Fe}^{3+} \] This shows that one dichromate ion oxidizes six ferrous ions.

Calculate the Change in Oxidation State

In the balanced equation, the change in oxidation number of chromium from +6 in ext{Cr}_2 ext{O}_7^{2-} to +3 in ext{Cr}^{3+} is calculated: \[ ext{Dichromate: } 2 imes (+6) ightarrow 2 imes (+3) \] The change is \((+6) - (+3) = 3\) for each chromium atom, and there are two chromium atoms, so the total change is \(2 imes 3 = 6\).

Determine the Number of Equivalents

The equivalence factor is determined by the change of 6 electrons for the reaction. The equivalent weight of a compound in redox reaction is calculated by the formula: \[ \text{Equivalent weight} = \frac{\text{Molar mass}}{\text{n-factor (change in oxidation number)}} \] For ext{Cr}_2 ext{O}_7^{2-}, the molar mass is 294 g and the n-factor is 6.

Calculate the Equivalent Weight

Plug the values from the previous steps into the formula: \[ \text{Equivalent weight} = \frac{294 \text{ g}}{6} = 49 \text{ g/equivalent} \] This is the equivalent weight of potassium dichromate.

Key concepts

Redox Reactions

Redox reactions, short for reduction-oxidation reactions, involve the transfer of electrons between two chemical species. The substance that loses electrons is said to be oxidized, while the substance that gains electrons is reduced. For example, in the provided reaction between dichromate ions and ferrous ions, the dichromate ions are reduced as they gain electrons, while the ferrous ions are oxidized as they lose electrons.

Understanding these reactions is crucial because they are the basis for a vast array of chemical processes, including combustion, respiration, and corrosion. In this exercise, potassium dichromate acts as the oxidizing agent because it receives electrons from the ferrous ions. The step-by-step electron transfer in the reactions makes it easier to balance even the most complex chemical reactions.

Here’s a key point to remember about redox reactions:

• Oxidation: Loss of electrons.
• Reduction: Gain of electrons.
• Oxidizing agent: Accepts electrons (gets reduced).
• Reducing agent: Donates electrons (gets oxidized).

Oxidation States

Oxidation states, or oxidation numbers, are essential for understanding redox reactions. They indicate the degree of oxidation of an atom in a chemical compound. It's a theoretical charge that an atom would have if the compound were composed of ions.

In the reaction between dichromate ion and ferrous ion, we see a change in the oxidation states of the chromium and iron ions. The oxidation state of chromium in the dichromate ion is +6, which decreases to +3 in the reaction, reflecting a gain of electrons. Meanwhile, the iron changes from +2 to +3 as it loses an electron.

Understanding oxidation states is pivotal for:

• Determining electron transfer.
• Balancing redox reactions.
• Predicting how substances will interact.

For any element, the change in oxidation state helps us determine the number of electrons transferred, which is crucial for computing equivalent weights in reactions.

Chemical Equations

Chemical equations represent the reactants and products in a chemical reaction. They must be balanced to obey the law of conservation of mass, meaning the number of atoms of each element must be equal on both sides of the equation.

Take the dichromate and ferrous ion reaction: \[ \text{Cr}_2\text{O}_7^{2-} + 14\text{H}^+ + 6\text{Fe}^{2+} \rightarrow 2\text{Cr}^{3+} + 7\text{H}_2\text{O} + 6\text{Fe}^{3+} \] This equation is balanced, showing that the same number of atoms for each element appears on both sides. Additionally, the charges are balanced, which is crucial in redox reactions.

The steps to balance chemical equations involve:

• Writing down the unbalanced equation.
• Calculating the number of atoms for each element.
• Adjusting coefficients to ensure an equal number of each type of atom and charge on both sides.

Balancing chemical equations ensures that the reaction accurately represents reality, respecting both mass and charge conservation.

Acidic Medium Reactions

Many redox reactions occur in acidic mediums, which can alter the course of the reaction. An acidic medium often provides H⁺ ions that participate in balancing both the chemical equation and the charges involved.

In our specific reaction with dichromate and ferrous ions, the acidic medium contributes 14 H⁺ ions that help balance the remaining elements and charges, enhancing the completion of the reduction-oxidation cycle.

Here’s why acidic mediums are significant:

• They facilitate reactions involving proton transfer.
• They help stabilize transition states.
• They are essential for reactions where water is a product, which can further aid in balancing chemical equations.

Acidic mediums often simplify balancing redox reactions as compared to neutral or basic conditions, making them a common choice in laboratory and industrial processes.