Versene, a chelating agent having chemical formula `C_(2)H_(4)N_(2)(C_(2)H_(4)O_(2)Na)_4`. If each mole of this compound could bind 1 mole fo `Ca^(2+)`, then the rating of pure versene expressed as mg of `CaCO_(3)` bound per g of chelating agent is

Options

A. 100 mg
B. 163 mg
C. 200 mg
D. 263 mg

Explanation

To solve the problem, we need to determine the rating of pure Versene expressed as mg of CaCO3 bound per gram of the chelating agent. Let's break this down step by step:

### Step 1: Understand the Chemical Formula
The chemical formula of Versene is given as \( C_2H_4N_2(C_2H_4O_2Na)_4 \). This indicates that each mole of Versene can bind 1 mole of \( Ca^{2+} \).

### Step 2: Determine the Molar Mass of Versene
To find the molar mass of Versene, we need to calculate the contributions from each element in the formula:

- **Carbon (C)**: There are 2 carbon atoms from \( C_2H_4N_2 \) and 8 carbon atoms from \( (C_2H_4O_2Na)_4 \) (4 groups of \( C_2 \)). Thus, total \( C = 2 + 8 = 10 \).
\[ \text{Molar mass of C} = 10 \times 12 = 120 \, \text{g/mol} \]

- **Hydrogen (H)**: There are 4 hydrogen atoms from \( C_2H_4N_2 \) and 16 hydrogen atoms from \( (C_2H_4O_2Na)_4 \) (4 groups of \( H_4 \)). Thus, total \( H = 4 + 16 = 20 \).
\[ \text{Molar mass of H} = 20 \times 1 = 20 \, \text{g/mol} \]

- **Nitrogen (N)**: There are 2 nitrogen atoms from \( C_2H_4N_2 \).
\[ \text{Molar mass of N} = 2 \times 14 = 28 \, \text{g/mol} \]

- **Oxygen (O)**: There are 8 oxygen atoms from \( (C_2H_4O_2Na)_4 \) (4 groups of \( O_2 \)).
\[ \text{Molar mass of O} = 8 \times 16 = 128 \, \text{g/mol} \]

- **Sodium (Na)**: There are 4 sodium atoms from \( (C_2H_4O_2Na)_4 \).
\[ \text{Molar mass of Na} = 4 \times 23 = 92 \, \text{g/mol} \]

Now, summing these contributions:
\[ \text{Molar mass of Versene} = 120 + 20 + 28 + 128 + 92 = 388 \, \text{g/mol} \]

### Step 3: Molar Mass of CaCO3
Next, we calculate the molar mass of \( CaCO_3 \):
- Calcium (Ca): 40 g/mol
- Carbon (C): 12 g/mol
- Oxygen (O): 16 g/mol (3 oxygen atoms)
\[ \text{Molar mass of CaCO}_3 = 40 + 12 + (3 \times 16) = 100 \, \text{g/mol} \]

### Step 4: Calculate the Rating
Since 1 mole of Versene binds 1 mole of \( Ca^{2+} \), it can also bind 1 mole of \( CaCO_3 \). Therefore, we can find out how much \( CaCO_3 \) can be bound by 1 gram of Versene.

1 mole of Versene (388 g) binds 1 mole of \( CaCO_3 \) (100 g). Thus, for 1 g of Versene:
\[ \text{Amount of } CaCO_3 \text{ bound} = \frac{100 \, \text{g}}{388 \, \text{g}} = 0.2577 \, \text{g} \]

### Step 5: Convert to mg
To express this in mg:
\[ 0.2577 \, \text{g} = 0.2577 \times 1000 \, \text{mg} = 257.7 \, \text{mg} \]

### Final Answer
The rating of pure Versene expressed as mg of \( CaCO_3 \) bound per g of chelating agent is **257.7 mg**.

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