A gas is filled in a container whose mass is 916.4 g. The mass of the gas plus container is found to be 917.64g. If the container can hold 1107 `cm^3` of water, find the density of the gas.

Answer

To find the density of the gas, we can follow these steps:

### Step 1: Calculate the Mass of the Gas
The mass of the gas can be calculated by subtracting the mass of the empty container from the total mass of the gas plus container.

\[ \text{Mass of gas} = \text{Mass of gas + container} - \text{Mass of container} \]

Given:
- Mass of the container = 916.4 g
- Mass of gas + container = 917.64 g

\[ \text{Mass of gas} = 917.64 \, \text{g} - 916.4 \, \text{g} = 1.24 \, \text{g} \]

### Step 2: Determine the Volume of the Gas
The volume of the gas is equal to the volume of the container, which is given as 1107 cm³.

\[ \text{Volume of gas} = 1107 \, \text{cm}^3 \]

### Step 3: Calculate the Density of the Gas
Density is defined as mass per unit volume. We can use the formula:

\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]

Substituting the values we have:

\[ \text{Density} = \frac{1.24 \, \text{g}}{1107 \, \text{cm}^3} \]

Calculating this gives:

\[ \text{Density} \approx 0.00112 \, \text{g/cm}^3 \]

### Final Answer
The density of the gas is approximately **0.00112 g/cm³**.

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