A sample of pure calcium weighing 1.35 g was quantitatively converted to 1.88 g of pure CaO . Atomic mass of calcium is

Options

A. 20
B. 40
C. 60
D. 30

Answer

To determine the atomic mass of calcium from the given data, we can follow these steps:

### Step 1: Understand the Reaction
Calcium (Ca) reacts with oxygen (O) to form calcium oxide (CaO). The reaction can be represented as:
\[ \text{Ca} + \frac{1}{2} \text{O}_2 \rightarrow \text{CaO} \]

### Step 2: Identify the Masses Given
- Mass of pure calcium (Ca) = 1.35 g
- Mass of pure calcium oxide (CaO) = 1.88 g

### Step 3: Calculate the Mass of Oxygen in CaO
To find the mass of oxygen in the calcium oxide, we can use the molar masses:
- Molar mass of Ca = \( x \) (which we are trying to find)
- Molar mass of O = 16 g/mol

The molar mass of CaO is:
\[ \text{Molar mass of CaO} = \text{Molar mass of Ca} + \text{Molar mass of O} = x + 16 \]

### Step 4: Set up the Mass Relationship
From the reaction, we know that:
1.35 g of Ca produces 1.88 g of CaO. We can set up a proportion:
\[ \frac{1.35 \, \text{g Ca}}{1.88 \, \text{g CaO}} = \frac{x}{x + 16} \]

### Step 5: Cross Multiply and Solve for x
Cross multiplying gives us:
\[ 1.35 (x + 16) = 1.88x \]

Expanding this:
\[ 1.35x + 21.6 = 1.88x \]

Now, rearranging the equation:
\[ 21.6 = 1.88x - 1.35x \]
\[ 21.6 = 0.53x \]

### Step 6: Solve for x
Now, divide both sides by 0.53 to find the atomic mass of calcium (x):
\[ x = \frac{21.6}{0.53} \approx 40.75 \]

### Step 7: Round to the Nearest Whole Number
The atomic mass of calcium is approximately 40.75 g/mol, which we round to 40 g/mol.

### Conclusion
The atomic mass of calcium is approximately **40 g/mol**.

---