Analysis shows that a binary compound of X (atomic mass =10) and Y (atomic mass =20) contains 50% X. What is the formula of the compound ?

Options

A. XY
B. `X_(2)Y`
C. `XY_(2)`
D. `X_(2)Y_(3)`

Explanation

To determine the formula of the binary compound composed of elements X and Y, we can follow these steps:

### Step 1: Understand the Given Information
- The atomic mass of element X = 10
- The atomic mass of element Y = 20
- The compound contains 50% of element X by mass.

### Step 2: Calculate the Mass of Each Element in the Compound
Since the compound contains 50% of X, we can assume a total mass of the compound for easier calculations. Let's assume the total mass of the compound is 100 grams. Therefore:
- Mass of X = 50% of 100g = 50g
- Mass of Y = 100g - 50g = 50g

### Step 3: Convert Mass to Moles
Next, we convert the mass of each element to moles using their atomic masses:
- Moles of X = Mass of X / Atomic mass of X = 50g / 10 g/mol = 5 moles
- Moles of Y = Mass of Y / Atomic mass of Y = 50g / 20 g/mol = 2.5 moles

### Step 4: Determine the Simplest Ratio
Now, we need to find the simplest whole number ratio of the moles of X and Y:
- Ratio of X to Y = Moles of X : Moles of Y = 5 : 2.5

To simplify this ratio, we can divide both sides by 2.5:
- Simplified ratio = 5 / 2.5 : 2.5 / 2.5 = 2 : 1

### Step 5: Write the Empirical Formula
From the simplified ratio, we can write the empirical formula of the compound:
- The empirical formula is X2Y.

### Conclusion
The formula of the compound is **X2Y**.

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