If a sample of a gas is initially at 755 mmHg 12.6L and 22.4 C what will be the new pressure if the volume is reduced by 2.5 L and the temperature is 33.3 C
To solve this problem, we can use the combined gas law formula:
P₁V₁/T₁ = P₂V₂/T₂
Where:
P₁ = initial pressure (755 mmHg)
V₁ = initial volume (12.6 L)
T₁ = initial temperature in Kelvin (22.4 °C + 273.15 = 295.55 K)
P₂ = unknown final pressure
V₂ = final volume (12.6 L - 2.5 L = 10.1 L)
T₂ = final temperature in Kelvin (33.3 °C + 273.15 = 306.45 K)
Plugging the given values into the formula, we get:
(755 mmHg)(12.6 L)/(295.55 K) = P₂(10.1 L)/(306.45 K)
Simplifying the equation, we have:
P₂ = (755 mmHg)(12.6 L)(306.45 K)/(295.55 K)(10.1 L)
P₂ ≈ 987 mmHg
Therefore, the new pressure of the gas, when the volume is reduced by 2.5 L and the temperature is increased to 33.3 °C, is approximately 987 mmHg.
To solve this problem, we can use the combined gas law equation:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where:
P1 = initial pressure (in mmHg)
V1 = initial volume (in L)
T1 = initial temperature (in Kelvin)
P2 = final pressure (unknown)
V2 = final volume (unknown)
T2 = final temperature (in Kelvin)
First, let's convert the given temperature values to Kelvin:
T1 = 22.4°C + 273.15 = 295.55 K
T2 = 33.3°C + 273.15 = 306.45 K
Now, we can substitute the given values into the equation:
(755 mmHg * 12.6 L) / 295.55 K = (P2 * (12.6 - 2.5) L) / 306.45 K
Next, we can solve for P2, the final pressure, by cross-multiplying and rearranging the equation:
(755 * 12.6) / 295.55 = (P2 * 10.1) / 306.45
(755 * 12.6 * 306.45) / (295.55 * 10.1) = P2
P2 ≈ 817.4 mmHg
Therefore, the new pressure would be approximately 817.4 mmHg if the volume is reduced by 2.5 L and the temperature increases to 33.3°C.
To find the new pressure of the gas, we can use the combined gas law formula, which relates the initial and final conditions of pressure, volume, and temperature.
The combined gas law formula is as follows: P₁V₁ / T₁ = P₂V₂ / T₂
Where:
P₁ = initial pressure
V₁ = initial volume
T₁ = initial temperature
P₂ = final pressure (what we want to find)
V₂ = final volume
T₂ = final temperature
Let's plug in the given values into the formula and solve for P₂:
P₁ = 755 mmHg
V₁ = 12.6 L
T₁ = 22.4 °C + 273.15 (convert from Celsius to Kelvin) = 295.55 K
V₂ = V₁ - 2.5 L (volume is reduced by 2.5 L)
T₂ = 33.3 °C + 273.15 (convert from Celsius to Kelvin) = 306.45 K
Now, we can substitute these values into the formula:
(755 mmHg)(12.6 L) / 295.55 K = P₂(12.6 L - 2.5 L) / 306.45 K
Simplifying the equation:
(9501 mmHg * L) / 295.55 K = (10.1P₂ mmHg * L) / 306.45 K
Cross-multiplying:
9501 * 306.45 K = 295.55 K * 10.1P₂
P₂ = (9501 * 306.45 K) / (295.55 K * 10.1)
Calculating:
P₂ ≈ 990.8 mmHg
Therefore, the new pressure of the gas will be approximately 990.8 mmHg.