A certain laser uses a gas mixture consisting of 9.0 grams of Hydrogen chloride, 2.0 grams Hydrogen gas, and 165.0 grams of Neon. What pressure is exerted by the mixture in a 75.0 liter tank at 22 degree Celsius? Which gas has the smallest partial pressure?
The long way is to use PV = nRT and solve for pressure of each gas. n = grams/molar mass or atomic mass when dealing with grams.
Then add the partial pressures to find the total pressure.
0.661
To determine the pressure exerted by the gas mixture in the tank, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles of gas
R = ideal gas constant (0.0821 L•atm/(mol•K))
T = temperature in Kelvin
First, we need to calculate the number of moles of each gas present in the mixture:
1. Hydrogen chloride (HCl):
Given mass of HCl = 9.0 grams
Molar mass of HCl = 36.46 g/mol
n(HCl) = mass/molar mass = 9.0 g / 36.46 g/mol = 0.2467 mol
2. Hydrogen gas (H2):
Given mass of H2 = 2.0 grams
Molar mass of H2 = 2.02 g/mol
n(H2) = mass/molar mass = 2.0 g / 2.02 g/mol = 0.9901 mol
3. Neon (Ne):
Given mass of Ne = 165.0 grams
Molar mass of Ne = 20.18 g/mol
n(Ne) = mass/molar mass = 165.0 g / 20.18 g/mol = 8.1722 mol
Now, let's sum up the number of moles of the gases to get the total number of moles (n) in the mixture:
Total moles (n) = n(HCl) + n(H2) + n(Ne) = 0.2467 mol + 0.9901 mol + 8.1722 mol = 9.4089 mol
Next, we need to convert the temperature from Celsius to Kelvin:
Temperature in Kelvin (T) = 22°C + 273.15 = 295.15 K
Now, we can substitute the values into the ideal gas law equation:
(9.4089 mol) * (0.0821 L•atm/(mol•K)) * (295.15 K) = P * (75.0 L)
Solving for P (pressure):
P = (9.4089 mol * 0.0821 L•atm/(mol•K) * 295.15 K) / 75.0 L
P ≈ 3.815 atm
The pressure exerted by the mixture in the 75.0 liter tank is approximately 3.815 atm.
To determine which gas has the smallest partial pressure, we need to compare the moles of each gas. The gas with the smallest moles will have the smallest partial pressure.
In this case, the gas with the smallest moles is Hydrogen chloride (HCl), with 0.2467 mol. Therefore, Hydrogen chloride (HCl) has the smallest partial pressure.
To determine the pressure exerted by the gas mixture, we need to apply the ideal gas law equation: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.
First, we need to calculate the number of moles (n) for each gas present in the mixture.
1. Hydrogen chloride (HCl):
To calculate the number of moles, we use the molar mass of HCl, which is 1.0 g/mol (hydrogen) + 35.5 g/mol (chlorine).
Number of moles of HCl = Mass of HCl / Molar mass of HCl
Number of moles of HCl = 9.0 g / (1.0 g/mol + 35.5 g/mol) = 0.225 mol
2. Hydrogen gas (H2):
Using the molar mass of hydrogen gas, which is 2.0 g/mol.
Number of moles of H2 = Mass of H2 / Molar mass of H2
Number of moles of H2 = 2.0 g / 2.0 g/mol = 1.0 mol
3. Neon (Ne):
The molar mass of neon is 20.18 g/mol.
Number of moles of Ne = Mass of Ne / Molar mass of Ne
Number of moles of Ne = 165.0 g / 20.18 g/mol = 8.18 mol
Now, let's calculate the total number of moles (n) in the mixture:
Total number of moles (n) = moles of HCl + moles of H2 + moles of Ne
Total number of moles (n) = 0.225 mol + 1.0 mol + 8.18 mol = 9.405 mol
Next, we need to convert the temperature from Celsius to Kelvin:
Temperature in Kelvin (T) = 22 °C + 273.15 = 295.15 K
Now, let's substitute the known values into the ideal gas law equation:
PV = nRT
P * 75.0 L = 9.405 mol * 0.0821 L·atm/(mol·K) * 295.15 K
Solving for P:
P = (9.405 mol * 0.0821 L·atm/(mol·K) * 295.15 K) / 75.0 L
P ≈ 3.651 atm
Therefore, the pressure exerted by the gas mixture in the 75.0 liter tank at 22 degrees Celsius is approximately 3.651 atm.
To determine which gas has the smallest partial pressure, we need to compare the moles of each gas present in the mixture.
Moles of HCl = 0.225 mol
Moles of H2 = 1.0 mol
Moles of Ne = 8.18 mol
Comparing the moles, we can see that the gas with the smallest amount (moles) is Hydrogen chloride (HCl) with 0.225 mol. Therefore, Hydrogen chloride has the smallest partial pressure in the mixture.