To determine the volume of 146.07 grams of a gas with a molar mass of 78.72 g/mol at standard temperature and pressure (STP), we'll proceed through a few systematic steps. Standard Temperature and Pressure (STP) is defined as a temperature of 0°C (273.15 K) and a pressure of 1 atmosphere, under which conditions one mole of an ideal gas occupies 22.414 liters.
### Step-by-Step Solution:
1. Calculate the number of moles of the gas:
The number of moles of a substance can be calculated using the formula:
[tex]\[
\text{moles of gas} = \frac{\text{mass of gas}}{\text{molar mass}}
\][/tex]
Given:
- Mass of the gas, [tex]\( m = 146.07 \)[/tex] grams
- Molar mass, [tex]\( M = 78.72 \)[/tex] g/mol
So,
[tex]\[
\text{moles of gas} = \frac{146.07 \text{ grams}}{78.72 \text{ g/mol}} \approx 1.856 \text{ moles}
\][/tex]
2. Calculate the volume occupied by the gas at STP:
At STP, one mole of an ideal gas occupies 22.414 liters. Therefore, the volume can be calculated using the formula:
[tex]\[
\text{volume} = \text{moles of gas} \times 22.414 \text{ L/mol}
\][/tex]
Using the number of moles calculated previously:
[tex]\[
\text{volume} = 1.856 \text{ moles} \times 22.414 \text{ L/mol} \approx 41.591 \text{ liters}
\][/tex]
3. Round to the nearest tenth:
When rounding 41.591 liters to the nearest tenth, we get:
[tex]\[
\text{volume rounded} \approx 41.6 \text{ liters}
\][/tex]
### Final Answer:
The volume of 146.07 grams of the gas with a molar mass of 78.72 g/mol at STP is approximately [tex]\( 41.6 \)[/tex] liters (rounded to the nearest tenth).
