The formula of an acid is `HXO_2`. The mass of `0.0242` g of the acid is `1.657g`. What is the atomic mass of X ?

Options

A. 35.5
B. 28.1
C. 128
D. 19

Answer

To find the atomic mass of element X in the acid with the formula \( HXO_2 \), we can follow these steps:

### Step 1: Calculate the number of moles of the acid
We know the mass of the acid and can use the formula for moles:

\[ \text{Moles} = \frac{\text{Mass}}{\text{Molar Mass}} \]

Given:
- Mass of the acid = 1.657 g
- Moles of the acid = 0.0242 mol

We can rearrange the formula to find the molar mass:

\[ \text{Molar Mass} = \frac{\text{Mass}}{\text{Moles}} = \frac{1.657 \, \text{g}}{0.0242 \, \text{mol}} \]

Calculating this gives:

\[ \text{Molar Mass} = 68.47 \, \text{g/mol} \]

### Step 2: Write the expression for the molar mass of the acid
The molar mass of the acid \( HXO_2 \) can be expressed in terms of the atomic mass of X:

\[ \text{Molar Mass} = \text{Atomic Mass of H} + \text{Atomic Mass of X} + 2 \times \text{Atomic Mass of O} \]

Using known atomic masses:
- Atomic mass of H = 1 g/mol
- Atomic mass of O = 16 g/mol

Substituting these values into the equation:

\[ 68.47 \, \text{g/mol} = 1 + X + 2 \times 16 \]

### Step 3: Simplify the equation
Now simplify the equation:

\[ 68.47 = 1 + X + 32 \]

Combining the constants:

\[ 68.47 = X + 33 \]

### Step 4: Solve for X
Now, isolate X:

\[ X = 68.47 - 33 \]
\[ X = 35.47 \, \text{g/mol} \]

### Conclusion
The atomic mass of element X is approximately \( 35.47 \, \text{g/mol} \).

---