Question

question 15
a sample of gas has a volume of 786 ml at a pressure of 1.27 atm and a temperature of 135°c. what is the pressure of the gas
when volume is changed to 500 ml and the temperature is changed to 250°c? pressure is
enter answer
atm
5 points

Explanation:

Step1: Convert temperatures to Kelvin

The formula to convert Celsius to Kelvin is \(T(K)=T(^{\circ}C)+273\).
For the initial temperature \(T_1 = 135^{\circ}C\), \(T_1=135 + 273=408K\).
For the final temperature \(T_2 = 250^{\circ}C\), \(T_2=250+ 273 = 523K\).

Step2: Use the combined gas law \(\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}\)

We are given \(P_1 = 1.27atm\), \(V_1 = 786mL\), \(V_2 = 500mL\), \(T_1 = 408K\), \(T_2 = 523K\).
Rearrange the formula for \(P_2\): \(P_2=\frac{P_1V_1T_2}{V_2T_1}\).
Substitute the values: \(P_2=\frac{1.27\times786\times523}{500\times408}\).
First, calculate the numerator: \(1.27\times786\times523=1.27\times411078 = 522069.06\).
Then, calculate the denominator: \(500\times408 = 204000\).
Now, \(P_2=\frac{522069.06}{204000}\approx2.56atm\).

Answer:

\(2.56\)