a 325ml sample of air is at 720 torr and 30.0 degrees Celsius. what volume will this gas occupy at 800 torr and 75.0 degrees Celsius.
thank you
To solve this problem, we will use the combined gas law formula:
(P1 × V1) / (T1) = (P2 × V2) / (T2)
where:
P1 = Initial pressure = 720 torr
V1 = Initial volume = 325 mL
T1 = Initial temperature = 30.0°C = 303.15 K
P2 = Final pressure = 800 torr
V2 = Final volume (to be calculated)
T2 = Final temperature = 75.0°C = 348.15 K
Let's substitute the given values into the equation:
(720 torr × 325 mL) / (303.15 K) = (800 torr × V2) / (348.15 K)
Cross-multiply and solve for V2:
(720 torr × 325 mL × 348.15 K) = (800 torr × V2 × 303.15 K)
V2 = (720 × 325 × 348.15) / (800 × 303.15)
V2 ≈ 98.828 mL
Therefore, at 800 torr and 75.0°C, the air sample will occupy approximately 98.828 mL of volume.
To solve this problem, we can use the combined gas law formula, which relates the pressure, volume, and temperature of a gas.
The combined gas law formula is written as:
(P₁ * V₁) / (T₁) = (P₂ * V₂) / (T₂)
Where:
- P₁ is the initial pressure
- V₁ is the initial volume
- T₁ is the initial temperature
- P₂ is the final pressure
- V₂ is the final volume
- T₂ is the final temperature
We are given:
- P₁ = 720 torr (initial pressure)
- V₁ = 325 ml (initial volume)
- T₁ = 30.0 degrees Celsius (initial temperature)
- P₂ = 800 torr (final pressure)
- T₂ = 75.0 degrees Celsius (final temperature)
Let's plug these values into the formula and solve for V₂:
(720 torr * 325 ml) / (30.0 degrees Celsius) = (800 torr * V₂) / (75.0 degrees Celsius)
We first need to convert the temperatures from Celsius to Kelvin by adding 273.15:
(720 torr * 325 ml) / (30.0 degrees Celsius + 273.15) = (800 torr * V₂) / (75.0 degrees Celsius + 273.15)
Let's solve for V₂:
(720 torr * 325 ml * (75.0 degrees Celsius + 273.15)) / (30.0 degrees Celsius + 273.15) = 800 torr * V₂
Now we can rearrange the equation to solve for V₂:
V₂ = (720 torr * 325 ml * (75.0 degrees Celsius + 273.15)) / (800 torr)
Plugging in the values and calculating:
V₂ = (720 torr * 325 ml * (75.0 + 273.15)) / (800 torr)
V₂ = (720 * 325 * 348.15) / 800
V₂ = 99,369.75 / 800
V₂ = 124.21 ml
Therefore, the volume of the gas will be approximately 124.21 ml at 800 torr and 75.0 degrees Celsius.