Question

A gas is found to have the formula \(|\mathrm{CO}|_{x}\). Its \(\mathrm{VD}\) is 70 . The value of \(x\) must be (1) 3 (2) 5 (3) 6 (4) \(2.5\)

Short answer

The value of \(x\) is 5.

Step-by-step solution

Understanding the Problem

Given the formula \(|\mathrm{CO}|_{x}\) and vapor density (\(\mathrm{VD}\)) of 70, the goal is to find the value of \(x\).

Formula for Molecular Weight Using Vapor Density

Recall the molecular weight (\( \mathrm{MW} \)) can be calculated from the vapor density using the formula: \[ \mathrm{MW} = 2 \times \mathrm{VD} = 2 \times 70 = 140 \]

Molecular Weight of the Given Compound

The molecular weight (\( \mathrm{MW} \)) of \(|\mathrm{CO}|_{x}\) is 140.

Calculating the Molecular Weight of the Compound in Terms of x

The molecular weight of \(|\mathrm{CO}|_{x}\) is given by: \[ \mathrm{MW} = x \times (\mathrm{atomic\,weight \ of\, C} + \mathrm{atomic\, weight\, of\, O}) = x \times (12 + 16) = x \times 28 \]

Equating and Solving for x

We know the molecular weight is 140: \[ x \times 28 = 140 \] Solve for \(x\): \[ x = \frac{140}{28} = 5 \]

Key concepts

Molecular Weight Calculation

When calculating the molecular weight of a compound, it's essential to understand the total weight of all atoms present in a molecule. Molecular weight (also called molecular mass) is the sum of the atomic weights of all the atoms in a molecule. To compute this:

1. First, identify the chemical formula for the compound. In our example, we have \(|\mathrm{CO}|_{x}\).
2. Break down the formula to determine the number of each type of atom. For \(|\mathrm{CO}|_{x}\), there is one carbon (\