An alloy consists of rubidium and one of the other alkali metals. A sample of `4.6g` of the alloy when allowed to react with water, liberates `2.241dm^(3)` of hydrogen at `STP`.
Relative atomic masses: `A_(T)(Li)=7,A_(T)(Na)=23,A_(T)(K)=39,A_(T)(Rb)=85.5,A_(T)(Cs)=1.33`
Which alkali metal is the component of the alloy?

Answer

To determine which alkali metal is present in the alloy with rubidium, we can follow these steps:

### Step-by-Step Solution:

1. **Write the Reaction Equation**:
The general reaction for an alkali metal (M) reacting with water is:
\[ M + H_2O \rightarrow MOH + \frac{1}{2}H_2 \]
In this reaction, one mole of the alkali metal reacts with water to produce one mole of metal hydroxide and half a mole of hydrogen gas.

2. **Calculate Moles of Hydrogen**:
We know that at STP (Standard Temperature and Pressure), 1 mole of any gas occupies 22.4 dm³. Given that 2.241 dm³ of hydrogen is liberated, we can calculate the number of moles of hydrogen produced:
\[ \text{Moles of } H_2 = \frac{2.241 \, \text{dm}^3}{22.4 \, \text{dm}^3/\text{mol}} = 0.1 \, \text{mol} \]

3. **Determine Moles of Alkali Metal**:
From the balanced equation, we see that 2 moles of the alkali metal react to produce 1 mole of hydrogen. Therefore, the moles of the alkali metal (M) will be:
\[ \text{Moles of M} = 2 \times \text{Moles of } H_2 = 2 \times 0.1 = 0.2 \, \text{mol} \]

4. **Calculate Mean Molar Mass of the Alloy**:
The mean molar mass of the alloy can be calculated using the formula:
\[ \text{Mean Molar Mass} = \frac{\text{Mass of Alloy}}{\text{Moles of M}} = \frac{4.6 \, \text{g}}{0.2 \, \text{mol}} = 23 \, \text{g/mol} \]

5. **Set Up the Equation for Molar Mass**:
The mean molar mass of the alloy is the weighted average of the molar masses of rubidium (Rb) and the other alkali metal (M):
\[ \text{Mean Molar Mass} = \frac{(85.5 \, \text{g/mol} \times x) + (M \, \text{g/mol} \times (1-x))}{1} \]
where \( x \) is the fraction of rubidium in the alloy. However, we can simplify this by recognizing that since the mean molar mass is 23 g/mol, we can deduce that the other alkali metal must have a molar mass that, when combined with rubidium, gives an average of 23 g/mol.

6. **Identify the Other Alkali Metal**:
Since the mean molar mass is 23 g/mol, we can compare it with the atomic masses of the other alkali metals:
- Lithium (Li) = 7 g/mol
- Sodium (Na) = 23 g/mol
- Potassium (K) = 39 g/mol
- Rubidium (Rb) = 85.5 g/mol
- Cesium (Cs) = 133 g/mol

The only alkali metal that can combine with rubidium to give an average of 23 g/mol is lithium (Li).

### Conclusion:
Therefore, the alkali metal present in the alloy along with rubidium is **Lithium (Li)**.