a gas have a volume of 100.0 ml when the temperature is -123C. What will its volume be at 27C? i don't know how to do it. can you help me please?
Certainly! To solve this problem, we can use the combined gas law, which states that the ratio of the initial and final volumes of a gas is equal to the ratio of the initial and final temperatures, assuming constant pressure.
The formula is:
(V1 / T1) = (V2 / T2)
Using this formula, we can determine the final volume (V2) when we know the initial volume (V1), the initial temperature (T1), and the final temperature (T2).
Let's calculate it step-by-step:
Given:
Initial volume (V1) = 100.0 ml
Initial temperature (T1) = -123°C
Final temperature (T2) = 27°C
Step 1: Convert temperatures to Kelvin
To use the equation, we need to convert the temperatures to Kelvin since the Kelvin scale uses absolute temperatures.
T1 in Kelvin = T1 in Celsius + 273.15
T2 in Kelvin = T2 in Celsius + 273.15
T1 in Kelvin = -123 + 273.15 = 150.15 K
T2 in Kelvin = 27 + 273.15 = 300.15 K
Step 2: Use the combined gas law equation to solve for V2
(V1 / T1) = (V2 / T2)
Substituting the given values:
(100.0 ml / 150.15 K) = (V2 / 300.15 K)
Step 3: Solve for V2
Cross-multiply the equation:
(100 ml * 300.15 K) = (V2 * 150.15 K)
(V2 * 150.15 K) = (100 ml * 300.15 K)
V2 = (100 ml * 300.15 K) / (150.15 K)
V2 ≈ 200 ml
Therefore, the volume of the gas at 27°C will be approximately 200.0 ml.