Question

a 8.2 l sample of gas has a pressure of 0.8 atm at a temperature of 259 k. if the temperature increases to 301 k, causing the volume to increase to 11.5 l, what is the new pressure? round your answer to the nearest tenth.
______ atm

Explanation:

Step1: Recall the Combined Gas Law

The Combined Gas Law is \(\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}\), where \(P_1 = 0.8\) atm, \(V_1 = 8.2\) L, \(T_1 = 259\) K, \(V_2 = 11.5\) L, \(T_2 = 301\) K, and we need to find \(P_2\).

Step2: Rearrange the formula to solve for \(P_2\)

From \(\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}\), we get \(P_2=\frac{P_1V_1T_2}{T_1V_2}\).

Step3: Substitute the given values

Substitute \(P_1 = 0.8\), \(V_1 = 8.2\), \(T_1 = 259\), \(T_2 = 301\), \(V_2 = 11.5\) into the formula:
\(P_2=\frac{0.8\times8.2\times301}{259\times11.5}\)

First, calculate the numerator: \(0.8\times8.2 = 6.56\), then \(6.56\times301 = 6.56\times300+6.56\times1 = 1968 + 6.56 = 1974.56\)

Then, calculate the denominator: \(259\times11.5 = 259\times(10 + 1.5)=2590+388.5 = 2978.5\)

Now, divide the numerator by the denominator: \(P_2=\frac{1974.56}{2978.5}\approx0.663\)

Step4: Round to the nearest tenth

Rounding \(0.663\) to the nearest tenth gives \(0.7\) (since the hundredth digit is 6, which is greater than or equal to 5, we round up the tenth digit).

Answer:

\(0.7\)