(a) `CuSO_(4).5H_(2)O(s)hArrCuSO_(4).3H_(2)O(s)+2H_(2)O(g) K_(p)=4xx10^(-4)atm^(2)`
(b) `Na_(2)SO_(4).10H_(2)O(s)hArrNa_(2)SO_(4).5H_(2)O(s)+5H_(2)O(g) K_(p)=2.43xx10^(-8) atm^(5)`
(c) `Na_(2)S_(2)O_(3).5H_(2)O(s)hArrNa_(2)S_(2)O_(3).2H_(2)O(s)+3H_(2)O(g) K_(p)=6.4xx10^(-5) atm^(3)`
What is order of vapour pressure and relative humidity respectively.

Options

A. `cgtbgta` V.P.
`cltblta R.H.`
B. `cltblta` V.P.
`cgtbgta R.H.`
C. `agtcgtb` V.P.
` agtcgtb R.H.`
D. `agtcgtb` V.P.
`altcltb R.H.`

Answer

To solve the problem, we need to determine the order of vapor pressure and relative humidity for the given reactions involving hydrates. Let's break it down step by step.

### Step 1: Understanding the Reactions
We have three reactions involving hydrates:
1. \( \text{CuSO}_4 \cdot 5\text{H}_2\text{O}(s) \rightleftharpoons \text{CuSO}_4 \cdot 3\text{H}_2\text{O}(s) + 2\text{H}_2\text{O}(g) \) with \( K_p = 4 \times 10^{-4} \, \text{atm}^2 \)
2. \( \text{Na}_2\text{SO}_4 \cdot 10\text{H}_2\text{O}(s) \rightleftharpoons \text{Na}_2\text{SO}_4 \cdot 5\text{H}_2\text{O}(s) + 5\text{H}_2\text{O}(g) \) with \( K_p = 2.43 \times 10^{-8} \, \text{atm}^5 \)
3. \( \text{Na}_2\text{S}_2\text{O}_3 \cdot 5\text{H}_2\text{O}(s) \rightleftharpoons \text{Na}_2\text{S}_2\text{O}_3 \cdot 2\text{H}_2\text{O}(s) + 3\text{H}_2\text{O}(g) \) with \( K_p = 6.4 \times 10^{-5} \, \text{atm}^3 \)

### Step 2: Calculating Vapor Pressure
The vapor pressure of the hydrate can be calculated using the formula:
\[ P = K_p^{\frac{1}{X}} \]
where \( X \) is the number of water molecules released in the reaction.

#### For Reaction (a):
- \( K_p = 4 \times 10^{-4} \, \text{atm}^2 \)
- \( X = 2 \)
\[ P_a = (4 \times 10^{-4})^{\frac{1}{2}} = \sqrt{4 \times 10^{-4}} = 2 \times 10^{-2} \, \text{atm} = 0.02 \, \text{atm} \]

#### For Reaction (b):
- \( K_p = 2.43 \times 10^{-8} \, \text{atm}^5 \)
- \( X = 5 \)
\[ P_b = (2.43 \times 10^{-8})^{\frac{1}{5}} \approx 0.03 \, \text{atm} \]

#### For Reaction (c):
- \( K_p = 6.4 \times 10^{-5} \, \text{atm}^3 \)
- \( X = 3 \)
\[ P_c = (6.4 \times 10^{-5})^{\frac{1}{3}} \approx 0.04 \, \text{atm} \]

### Step 3: Ordering the Vapor Pressures
Now we can compare the calculated vapor pressures:
- \( P_a = 0.02 \, \text{atm} \)
- \( P_b = 0.03 \, \text{atm} \)
- \( P_c = 0.04 \, \text{atm} \)

Thus, the order of vapor pressure is:
\[ P_a < P_b < P_c \quad \text{(or A < B < C)} \]

### Step 4: Calculating Relative Humidity
Relative humidity (RH) is defined as:
\[ \text{RH} = \frac{\text{Actual Vapor Pressure}}{\text{Saturation Vapor Pressure}} \times 100 \]

Since the actual vapor pressure is the same as the calculated vapor pressures and the saturation vapor pressure increases with decreasing vapor pressure, we can conclude:
- The order of relative humidity will be the inverse of the order of vapor pressure:
\[ \text{RH}_a > \text{RH}_b > \text{RH}_c \quad \text{(or A > B > C)} \]

### Final Answer
- **Order of Vapor Pressure:** \( A < B < C \)
- **Order of Relative Humidity:** \( A > B > C \)