To find the final temperature when the volume changes from 2.1 L to 16 L at a pressure of 1.9 atm after initially being at 3.7 atm, 2.1 L, and 63°C, we can use the combined gas law formula, which is:
\[\frac{P_1 \times V_1 \times T_2}{P_2 \times V_2} = T_1\]
1. Identify the given values:
- Initial pressure, \(P_1 = 3.7\) atm
- Initial volume, \(V_1 = 2.1\) L
- Initial temperature, \(T_1 = 63\)°C or 336 K (convert to Kelvin by adding 273)
- Final pressure, \(P_2 = 1.9\) atm
- Final volume, \(V_2 = 16\) L
2. Substitute the values into the formula and solve for the final temperature, \(T_2\):
\[\frac{3.7 \times 2.1 \times 336}{1.9 \times 16} = T_2\]
3. Calculate the final temperature, \(T_2\), by performing the math:
\[\frac{2646.72}{30.4} = T_2\]
\[T_2 ≈ 87.09 \text{ K}\]
Therefore, when the volume changes to 16 L at a pressure of 1.9 atm, the final temperature would be approximately 87.09 K.
