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Gas Laws Fact Sheet

| Concept | Formula |
|-------------------------------|-----------------------------------|
| Ideal gas law | [tex]\( PV = nRT \)[/tex] |
| Ideal gas constant | [tex]\( R = 8.314 \frac{L \cdot kPa}{mol \cdot K} \)[/tex] or [tex]\( R = 0.0821 \frac{L \cdot atm}{mol \cdot K} \)[/tex] |
| Standard atmospheric pressure | [tex]\( 1 \, atm = 101.3 \, kPa \)[/tex] |
| Celsius to Kelvin conversion | [tex]\( K = {}^\circ C + 273.15 \)[/tex] |

Select the correct answer:

The gas in a sealed container has an absolute pressure of 9.25 atmospheres. If the air around the container is at standard pressure, what is the gauge pressure inside the container?

A. [tex]\( 0.759 \, atm \)[/tex]

B. [tex]\( 8.25 \, atm \)[/tex]

C. [tex]\( 10.25 \, atm \)[/tex]

D. [tex]\( 113 \, atm \)[/tex]

Sagot :

GinnyAnswer
To determine the gauge pressure inside the container, we first need to understand the difference between absolute pressure and gauge pressure.

1. Absolute Pressure: This is the total pressure exerted by the gas, including atmospheric pressure.
2. Gauge Pressure: This is the pressure of the gas relative to atmospheric pressure. It is essentially the additional pressure exerted by the gas over and above the atmospheric pressure.

Given:
- Absolute pressure inside the container: [tex]\(9.25\)[/tex] atmospheres
- Standard atmospheric pressure: [tex]\(1\)[/tex] atmosphere

To find the gauge pressure, we use the formula:
[tex]\[ \text{Gauge Pressure} = \text{Absolute Pressure} - \text{Atmospheric Pressure} \][/tex]

Substituting the given values:
[tex]\[ \text{Gauge Pressure} = 9.25 \, \text{atm} - 1 \, \text{atm} \][/tex]
[tex]\[ \text{Gauge Pressure} = 8.25 \, \text{atm} \][/tex]

Thus, the gauge pressure inside the container is [tex]\(8.25\)[/tex] atmospheres.

The correct answer is:
[tex]\[ \boxed{B. \, 8.25 \, \text{atm}} \][/tex]
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