a sample of nitrogen gas contain 5.0mol in a volume of 3.5L calculate the new volume of the container if the pressure and temperature are kept constant but the number of moles of nitrogen is change to 2.5 mol
Jiskha doesn't have any experts in san jac.
V proportional to n
V = 3.5 when n = 5
Therefore, if n = 2.5, V must be ...?
To find the new volume of the container, we can use the ideal gas law equation: PV = nRT, where:
P = Pressure (constant)
V = Volume (initial and final)
n = Number of moles of gas (initial and final)
R = Ideal gas constant
T = Temperature (constant)
Since the pressure and temperature are kept constant, we can rewrite the equation as:
V₁/n₁ = V₂/n₂
Given:
n₁ = 5.0 mol (initial number of moles)
V₁ = 3.5 L (initial volume)
n₂ = 2.5 mol (new number of moles)
We can rearrange the equation and solve for V₂:
V₂ = (V₁ * n₂) / n₁
Substituting the given values into the equation:
V₂ = (3.5 L * 2.5 mol) / 5.0 mol
V₂ = 1.75 L
Therefore, the new volume of the container is 1.75 L.
To find the new volume of the container, you can use Boyle's Law, which states that the product of pressure and volume is constant as long as the temperature remains constant.
Mathematically, the equation can be written as:
P₁V₁ = P₂V₂
Where:
P₁ = initial pressure (constant)
V₁ = initial volume (given as 3.5L)
P₂ = final pressure (constant)
V₂ = final volume (to be calculated)
Now, we can rearrange the equation to solve for V₂:
V₂ = (P₁V₁) / P₂
Since the pressure and temperature are kept constant, the moles change will only affect the volume.
So, we can substitute the initial and final number of moles into Avogadro's Law, which states that equal volumes of gases, at the same temperature and pressure, contain an equal number of particles (moles).
Mathematically, the equation can be written as:
V₁ / n₁ = V₂ / n₂
Where:
V₁ = initial volume (given as 3.5L)
n₁ = initial number of moles (given as 5.0 mol)
V₂ = final volume (to be calculated)
n₂ = final number of moles (given as 2.5 mol)
Now, we can rearrange the equation to solve for V₂:
V₂ = (V₁ * n₂) / n₁
Substituting the given values into the equation, we get:
V₂ = (3.5L * 2.5mol) / 5.0mol
V₂ = 1.75L
Therefore, the new volume of the container, when the number of moles of nitrogen is changed to 2.5 mol, while keeping the pressure and temperature constant, is 1.75L.