A container has hydrogen and oxygen mixture in ratio of 4 : 1 by weight, then

Options

A. Internal energy of the mixture decreases
B. Internal energy of the mixture increases
C. Entropy of the mixture increases
D. Entropy of the mixture decreases

Explanation

To solve the problem step by step, we need to analyze the reaction between hydrogen and oxygen and its effects on internal energy and entropy.

### Step 1: Identify the Reaction
The reaction between hydrogen (H₂) and oxygen (O₂) can be represented as:
\[ 2H_2 + O_2 \rightarrow 2H_2O \]
This indicates that two moles of hydrogen react with one mole of oxygen to produce two moles of water.

**Hint:** Remember that the stoichiometry of the reaction is crucial for determining the amounts of reactants and products involved.

### Step 2: Determine the Ratio by Weight
Given that the mixture of hydrogen and oxygen is in the ratio of 4:1 by weight, we can calculate the moles of each gas.

- Molar mass of H₂ = 2 g/mol
- Molar mass of O₂ = 32 g/mol

If we assume we have 4g of H₂, then the weight of O₂ would be 1g.

Calculating moles:
- Moles of H₂ = \( \frac{4g}{2g/mol} = 2 \) moles
- Moles of O₂ = \( \frac{1g}{32g/mol} = 0.03125 \) moles

**Hint:** Use molar masses to convert grams to moles for each substance involved in the reaction.

### Step 3: Analyze the Reaction
In the reaction, 2 moles of H₂ react with 1 mole of O₂ to produce 2 moles of H₂O. Since we have excess hydrogen (2 moles of H₂ can react with only 0.03125 moles of O₂), the reaction will proceed until all the available O₂ is consumed.

**Hint:** Identify the limiting reactant to understand how much product can be formed and how it affects the system.

### Step 4: Determine Internal Energy Change
The formation of water from hydrogen and oxygen is an exothermic reaction, meaning it releases energy. Therefore, the internal energy of the system decreases as energy is released during the formation of water.

**Hint:** Recall that exothermic reactions result in a decrease in internal energy, while endothermic reactions would increase it.

### Step 5: Analyze Entropy Change
Entropy (S) is a measure of disorder in a system. In this reaction, we start with three moles of gas (2 moles of H₂ and 1 mole of O₂) and end up with 2 moles of liquid water (H₂O). The transition from gas to liquid represents a decrease in disorder, which means the entropy of the system decreases.

**Hint:** Consider the physical states of the reactants and products; gases have higher entropy than liquids.

### Conclusion
1. **Internal Energy:** Decreases (exothermic reaction).
2. **Entropy:** Decreases (transition from gas to liquid).

**Final Answer:** The internal energy of the system decreases, and the entropy of the mixture decreases.