A gas cylinder containing 6.38 mol of neon has a pressure of 491 mm Hg at 295 K. If 3.22 mol of helium is added to this cylinder, at constant temperature and volume, what will be the pressure in the cylinder?
PV=nRt
at constant volume and temp
P1/P2=n1/N2
P1=491mmHg*(6.38+3.22)/6.38
738.81
To find the pressure after the helium is added, we can use the ideal gas law equation:
PV = nRT
Where:
P = Pressure
V = Volume
n = number of moles
R = gas constant
T = Temperature
We will assume that the volume and temperature of the cylinder remain constant.
Given information:
Initial pressure of neon (P1) = 491 mm Hg
Number of moles of neon (n1) = 6.38 mol
To find the pressure after helium is added, we can set up the equation like this:
(P1)(V) = (n1 + n2)(R)(T)
where n2 is the number of moles of helium added.
We can rearrange the equation to solve for the final pressure:
P2 = (P1)(V) / (n1 + n2)
Substituting the given values:
P2 = (491 mm Hg)(V) / (6.38 mol + 3.22 mol)
Now we can calculate the final pressure:
P2 = (491 mm Hg)(V) / 9.60 mol
Since the volume and temperature remain the same, we can assume V is constant. So we can simply divide the numerator by the denominator:
P2 = (491 mm Hg) / 9.60
Calculating:
P2 ≈ 51.15 mm Hg
Therefore, the pressure in the cylinder after adding 3.22 mol of helium will be approximately 51.15 mm Hg.
To solve this problem, we can use the ideal gas law equation:
PV = nRT
Where:
P is the pressure of the gas
V is the volume of the gas
n is the amount of gas in moles
R is the ideal gas constant (0.0821 L·atm/(K·mol))
T is the temperature in Kelvin
We are given the pressure of the neon gas (P1), the number of moles of neon (n1), and the number of moles of helium (n2). We need to find the final pressure of the mixture (P2) when helium is added to the cylinder.
First, let's calculate the volume (V) of the gas. However, the volume is not given explicitly. The problem states that the temperature (T) and volume (V) are constant, which implies that the volume does not change.
Since we are assuming constant volume, the volume can cancel out in our equation. That means we'll only need the pressure, number of moles, and temperature.
Now let's calculate the initial pressure (P1) of the neon gas:
P1 = 491 mm Hg
We also need to convert the pressure from mm Hg to atm since the ideal gas constant (R) is given in atm:
1 atm = 760 mm Hg
So, P1 = 491 mm Hg * (1 atm/760 mm Hg) = 0.645 atm
Next, we'll calculate the total number of moles of gas (ntotal) in the cylinder:
ntotal = n1 + n2
ntotal = 6.38 mol + 3.22 mol = 9.6 mol
Now we can use the ideal gas law equation to find the final pressure (P2):
PV = nRT
Since the volume is constant, we can rewrite the equation as:
P1 * V = ntotal * R * T
Solving for P2 (final pressure):
P2 = (ntotal * R * T) / V
Plugging in the values:
P2 = (9.6 mol * 0.0821 L·atm/(K·mol) * 295 K) / V
Since the volume is constant, we can ignore it. Thus, we get:
P2 = 2.4 atm
So, the final pressure in the cylinder after adding helium will be 2.4 atm.