Question

5 numeric 1 point an unknown volume of gas is held at a temperature of 115 k in a container with a pressure of 60 atm. if by increasing the temperature to 225 k and decreasing the pressure to 30 atm causes the volume of the gas to be 29 liters, how many liters of gas were present to begin with? round to 3 sig figs. do not include units. answer previous next

Explanation:

Step1: Use the combined gas law

The combined gas law is \(\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}\). We need to solve for \(V_1\).

Step2: Rearrange the formula for \(V_1\)

\(V_1=\frac{P_2V_2T_1}{P_1T_2}\)

Step3: Substitute the given values

Given \(P_1 = 60\), \(T_1=115\), \(P_2 = 30\), \(T_2 = 225\), \(V_2=29\).
\(V_1=\frac{30\times29\times115}{60\times225}\)

Step4: Calculate the value

First, calculate the numerator: \(30\times29\times115 = 30\times3335=100050\)
Then, calculate the denominator: \(60\times225 = 13500\)
\(V_1=\frac{100050}{13500}\approx 7.41\)

Answer:

\(7.41\)