Question

What is the final pressure, in atmospheres, when the fire extinguisher is used at a temperature of 71 deg C if V and n do not change? Express your answer to two significant figures and include the appropriate units.

Answer 1

To find the final pressure, we can use Gay-Lussac's Law, which states that the pressure of a given amount of gas at constant volume is directly proportional to its temperature.

The formula for Gay-Lussac's Law is:
P1 / T1 = P2 / T2

where P1 and T1 are the initial pressure and temperature, and P2 and T2 are the final pressure and temperature.

Let's assume P1 is the initial pressure of the fire extinguisher and T1 is the initial temperature, and P2 is the final pressure and T2 is the final temperature.

Since the question states that V (volume) and n (amount) do not change, we can cancel out those variables from the equation.

So, we have:
P1 / T1 = P2 / T2

Plugging in the given values:
P1 / (273 + T1) = P2 / (273 + T2)

Assuming the initial temperature T1 is 20°C (since it is not given in the question), we have:
P1 / (273 + 20) = P2 / (273 + 71)

Simplifying the equation:
P1 / 293 = P2 / 344

Cross-multiplying:
P1 * 344 = P2 * 293

Rearranging the equation to solve for P2:
P2 = (P1 * 344) / 293

Now, we can plug in the known values to calculate P2:
P2 = (P1 * 344) / 293

Since the question asks for the final pressure in atmospheres, we can assume that the initial pressure P1 is given in atmospheres.

The final pressure P2 would be in atmospheres as well, since P1 is already in atmospheres and the units cancel out during the calculation.

Therefore, the final pressure is:
P2 = (P1 * 344) / 293

Remember to express the final answer to two significant figures.