`10 mg` of an adsorbate gets adsorbed on a surface. This cause the release of `3J` of heat constant pressure and at `27^(@)C`. `["Molar mass of adsorbate" =100 g//mol]`.
(i) Find `DeltaH_(AD)`
(ii) Argue whether the adsorption is physical or chemical?
(iii) If `20` mg of adsorbate is adsorbed a temperature `T_(0)`. Then compare `T_(0)` and `27^(@)C`.

Explanation

To solve the problem step by step, we will address each part of the question sequentially.

### Given Data:
- Mass of adsorbate = 10 mg = \(10 \times 10^{-3}\) g = \(10^{-2}\) g
- Heat released (Q) = 3 J
- Molar mass of adsorbate = 100 g/mol
- Temperature = 27°C

### (i) Finding \(\Delta H_{AD}\)

1. **Convert mass of adsorbate to moles**:
\[ \text{Number of moles} (n) = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]
\[ n = \frac{10 \times 10^{-3} \text{ g}}{100 \text{ g/mol}} = 10^{-4} \text{ mol} \]

2. **Calculate \(\Delta H_{AD}\)**:
The enthalpy change for adsorption can be calculated using the formula:
\[ \Delta H_{AD} = \frac{Q}{n} \]
Here, \(Q\) is the heat released, which is -3 J (since heat is released, it is negative in thermodynamic terms).
\[ \Delta H_{AD} = \frac{-3 \text{ J}}{10^{-4} \text{ mol}} = -30000 \text{ J/mol} = -30 \text{ kJ/mol} \]

### (ii) Argument on whether the adsorption is physical or chemical

- The enthalpy change (\(\Delta H_{AD}\)) we calculated is negative, which indicates that the process is exothermic.
- Typically, physical adsorption (physisorption) has a lower enthalpy change (usually in the range of -20 to -40 kJ/mol), while chemical adsorption (chemisorption) has a higher enthalpy change (greater than -40 kJ/mol).
- Since \(\Delta H_{AD} = -30 \text{ kJ/mol}\), we can conclude that the adsorption is likely **physical** (physisorption).

### (iii) Comparison of \(T_0\) and \(27°C\) when 20 mg of adsorbate is adsorbed

1. **Understanding the relationship between adsorption and temperature**:
- The amount of substance adsorbed is inversely proportional to temperature. This means that as the temperature increases, the amount of substance that can be adsorbed decreases.

2. **Given that 20 mg of adsorbate is adsorbed**:
- Since 20 mg is greater than 10 mg, and we know that the amount adsorbed is inversely related to temperature, it follows that:
\[ T_0 < 27°C \]

### Summary of Results:
- (i) \(\Delta H_{AD} = -30 \text{ kJ/mol}\)
- (ii) The adsorption is physical (physisorption).
- (iii) \(T_0 < 27°C\).