HELP PLEASE
the volume of a sample of oxygen is 200.0ml when the pressure is 3.00atm and the temp is 37.0 C. What is the new temp if the volume increases to 400.0ml and the pressure decreases to 2.000 atm?
To find the new temperature, we can use the combined gas law, which states:
(P1 × V1) / T1 = (P2 × V2) / T2
Where:
P1 = initial pressure = 3.00 atm
V1 = initial volume = 200.0 ml
T1 = initial temperature = 37.0°C + 273.15 (convert to Kelvin)
P2 = final pressure = 2.000 atm
V2 = final volume = 400.0 ml
T2 = final temperature (what we need to find)
First, let's convert the initial temperature from Celsius to Kelvin:
T1 = 37.0°C + 273.15 = 310.15 K
Then we can plug these values into the formula:
(3.00 atm × 200.0 ml) / 310.15 K = (2.000 atm × 400.0 ml) / T2
To solve for T2, we can rearrange the equation:
T2 = (2.000 atm × 400.0 ml) / ((3.00 atm × 200.0 ml) / 310.15 K)
Let's calculate T2:
T2 = (2.000 atm × 400.0 ml) / ((3.00 atm × 200.0 ml) / 310.15 K)
T2 ≈ 413.43 K
So, the new temperature is approximately 413.43 Kelvin.
To solve this problem, we can use the combined gas law equation, which relates the initial and final states of a gas:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where:
P1 = initial pressure
V1 = initial volume
T1 = initial temperature (in Kelvin)
P2 = final pressure
V2 = final volume
T2 = final temperature (in Kelvin)
Let's solve the problem step by step.
Step 1: Convert the temperatures to Kelvin.
The equation requires temperatures in Kelvin, so we need to convert the initial temperature of 37.0°C to Kelvin.
T1 = 37.0°C + 273.15 = 310.15 K
Step 2: Plug in the known values into the combined gas law equation.
(P1 * V1) / T1 = (P2 * V2) / T2
Substituting the given values:
(3.00 atm * 200.0 mL) / (310.15 K) = (2.000 atm * 400.0 mL) / T2
Step 3: Solve for T2.
To solve for T2, we rearrange the equation to isolate T2:
T2 = [(2.000 atm * 400.0 mL * 310.15 K) / (3.00 atm * 200.0 mL)]
Calculating the value, we have:
T2 = 413.53 K
Step 4: Convert the temperature back to Celsius (if needed).
If you want the temperature in Celsius, you can convert it back from Kelvin by subtracting 273.15:
T2 = 413.53 K - 273.15 = 140.38°C
Therefore, the new temperature (T2) is approximately 140.38°C.
(P1V1/T1) = (P2V2/T2)
Remember T must be in kelvin.