`6.022 xx 10^22` molecules of compound X has mass 10g.What is molarity of solution containing 5g of 'X' in 2 Lit. solution answer as P(where `M = P xx 10^(-3) mol / lit `)

Answer

To solve the problem step by step, we need to find the molarity of a solution containing 5g of compound X in 2 liters of solution. We know that 6.022 x 10^22 molecules of compound X has a mass of 10g.

### Step 1: Calculate the number of moles in 10g of compound X.
We know that:
- 6.022 x 10^22 molecules correspond to 10g of compound X.

Using Avogadro's number, we can find the number of moles:
\[ \text{Number of moles} = \frac{\text{Number of molecules}}{6.022 \times 10^{23}} \]
Since 6.022 x 10^22 molecules corresponds to 10g, we can express the number of moles as:
\[ \text{Number of moles} = \frac{6.022 \times 10^{22}}{6.022 \times 10^{23}} = \frac{1}{10} \text{ moles} \]

### Step 2: Find the molecular mass of compound X.
We can use the formula for the number of moles:
\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molecular mass (g/mol)}} \]
From Step 1, we have:
\[ \frac{10 \text{ g}}{M_X} = \frac{1}{10} \]
Cross-multiplying gives:
\[ M_X = 10 \text{ g} \times 10 = 100 \text{ g/mol} \]

### Step 3: Calculate the number of moles in 5g of compound X.
Now, we need to find the number of moles in 5g of compound X using the molecular mass we just calculated:
\[ \text{Number of moles} = \frac{\text{mass}}{\text{molecular mass}} = \frac{5 \text{ g}}{100 \text{ g/mol}} = 0.05 \text{ moles} \]

### Step 4: Calculate the molarity of the solution.
Molarity (M) is defined as the number of moles of solute per liter of solution:
\[ M = \frac{\text{Number of moles}}{\text{Volume (L)}} \]
Substituting the values we have:
\[ M = \frac{0.05 \text{ moles}}{2 \text{ L}} = 0.025 \text{ M} \]

### Step 5: Express the molarity in the form of P x 10^(-3) mol/L.
We need to express 0.025 M in the form of P x 10^(-3) mol/L:
\[ 0.025 = P \times 10^{-3} \]
To find P:
\[ P = 0.025 \times 10^3 = 25 \]

### Final Answer:
Thus, the value of P is 25.

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