Question

If 214.0 mL of a gas at 616.20 mmHg and 11.9°C is heated in a flexible container, and the final pressure ismeasured at 261.90 mmHg with an expanded volume of 512.0 mL, what is the final temperature of this gasin degrees Celsius?(Show all work)A) 333B) 16.7C) 290D) 14.0

Answer 1

B) 16.7

The final temperature of this gas in degrees Celsius = 16.7 °C

Step-by-step explanation

Given:

Initial volume, V₁ = 214.0 mL

Initial pressure, P₁ = 616.20 mmHg

Initial temperature, T₁ = 11.9 °C

Final pressure, P₂ = 261.90 mmHg

Final volume, V₂ = 512.0 mL

What to find:

The final temperature of this gas in degrees Celsius.

Step-by-step solution:

The first step is to convert the temperature to K.

Conversion factor:

0 °C = 0 + 273.15 K

∴ T₁ = 11.9 °C = 11.9 + 273 K = 285.05 K

The next step is to calculate the final temperature in K using the combined gas equation.

`\begin{gathered} (P_1V_1)/(T_1)=(P_2V_2)/(T_2) \\ \\ \Rightarrow T_2=(P_2V_2T_1)/(P_1V_1)=(261.90mmHg*512mL*285.05K)/(616.20mmHg*214mL)=289.86\text{ }K \end{gathered}`

The final step is to convert 289.86 K to °C.

Conversion factor:

0 K - 273.15 = -273.15 °C

Therefore, 289.86 - 273.15 = 16.71 °C = 16.7 °C

The final temperature of this gas in degrees Celsius is 16.7 °C