(a) What is the gauge pressure in a 25.0^∘ C car tire containing 3.60 mol of gas in a 30.0 L vol

step 1 Using p is equal to N r t divided by B so pressure p is equal to N times r times t divided by b

(a) What is the gauge pressure in a 25.0^∘ C car tire...

(a) What is the gauge pressure in a $25.0^{\circ} \mathrm{C}$ car tire containing 3.60 mol of gas in a 30.0 L volume? (b) What will its gauge pressure be if you add 1.00 L of gas originally at atmospheric pressure and $25.0^{\circ} \mathrm{C}$ ? Assume the temperature returns to $25.0^{\circ} \mathrm{C}$ and the volume remains constant.

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Key Concepts

Gas Addition in a Constant Volume, Constant Temperature System

When a gas is added to a system where the volume and temperature remain constant, the increase in the total number of gas moles leads directly to an increase in pressure as indicated by the ideal gas law. This concept is essential for understanding how modifications, like introducing additional gas under specified conditions, alter the pressure inside containers.

Ideal Gas Law (PV = nRT)

The ideal gas law connects pressure, volume, temperature, and number of moles of a gas using the equation PV = nRT. It provides a framework to predict how changes in one variable affect the others under the assumption of ideal behavior, which is crucial for solving problems involving gas pressures in confined volumes.

Gauge Pressure vs. Absolute Pressure

Gauge pressure is defined as the difference between the absolute pressure of a system and the ambient atmospheric pressure. In practical applications such as measuring tire pressure, understanding this distinction allows for the correct interpretation and calculation of the pressure that is actually exerted by the gas within the system.

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