Question

calculating the temperature of a gas
a 7 l sample of gas has a pressure of 1.1 atm at a temperature of 285 k. if the pressure decreases to 0.6 atm, causing the volume to increase to 10 l, what is the new temperature? round your answer to the nearest tenth.
k

Explanation:

Step1: Recall Combined Gas Law

The combined gas law is \(\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}\), where \(P_1 = 1.1\) atm, \(V_1 = 7\) L, \(T_1 = 285\) K, \(P_2 = 0.6\) atm, \(V_2 = 10\) L, and we need to find \(T_2\).

Step2: Rearrange for \(T_2\)

Rearrange the formula to solve for \(T_2\): \(T_2=\frac{P_2V_2T_1}{P_1V_1}\)

Step3: Substitute Values

Substitute the values: \(T_2=\frac{0.6\times10\times285}{1.1\times7}\)

Step4: Calculate Numerator and Denominator

First, calculate the numerator: \(0.6\times10\times285 = 6\times285 = 1710\)
Then, calculate the denominator: \(1.1\times7 = 7.7\)

Step5: Divide to Find \(T_2\)

Now, divide: \(T_2=\frac{1710}{7.7}\approx222.1\) (rounded to the nearest tenth)

Answer:

\(222.1\)