The density of a gas containing chlorine and oxygen has a density of 2.875 g/L at 754.5 mm Hg and 11(degress C). What is the most likely molecular formula of the gas?
To determine the most likely molecular formula of the gas, we need to use the ideal gas law equation:
PV = nRT
Where:
P = pressure of the gas (in atm or mm Hg)
V = volume of the gas (in liters)
n = number of moles of gas
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature of the gas (in Kelvin)
First, let's convert the given pressure of 754.5 mm Hg into atm:
754.5 mm Hg * (1 atm / 760 mm Hg) = 0.9932 atm
Next, let's convert the given temperature of 11 degrees Celsius into Kelvin:
11 degrees Celsius + 273.15 = 284.15 K
Now we can rearrange the ideal gas law equation to solve for the number of moles (n) of gas:
n = PV / RT
n = (0.9932 atm) * (V / (0.0821 L·atm/mol·K)) / (284.15 K)
The volume (V) is given as 1 L (since the density is given in grams per liter).
Calculating n:
n = (0.9932 atm) * (1 L / (0.0821 L·atm/mol·K)) / (284.15 K) = 0.04494 mol
Now, let's determine the molar mass of the gas using the provided density:
Density (d) = mass / volume
Rearranging the equation to solve for mass:
mass = density * volume
mass = 2.875 g/L * 1 L = 2.875 g
Next, we calculate the molar mass (M) using the number of moles (n) and mass (m):
Molar mass (M) = mass (m) / moles (n)
M = 2.875 g / 0.04494 mol ≈ 64 g/mol
Now, we can compare the molar mass (M) to the known molar masses of elements to determine the most likely molecular formula. In this case, we need to consider the molar masses of chlorine (Cl) and oxygen (O).
The molar mass of chlorine (Cl) is approximately 35.5 g/mol, while the molar mass of oxygen (O) is approximately 16 g/mol.
Let's calculate the possible combinations based on these molar masses:
1. One chlorine atom:
M = 35.5 g/mol
This leaves a difference of (64 g/mol - 35.5 g/mol) = 28.5 g/mol.
2. Two oxygen atoms:
2 * M = 2 * 16 g/mol = 32 g/mol
This leaves a difference of (64 g/mol - 32 g/mol) = 32 g/mol.
Based on the given molar mass and comparisons, the most likely molecular formula for the gas containing chlorine and oxygen is ClO2, where there are one chlorine atom and two oxygen atoms.
To determine the molecular formula of the gas, we first need to calculate the molar mass of the gas using the information provided.
Step 1: Convert the given temperature from degrees Celsius to Kelvin.
To convert Celsius to Kelvin, we use the formula: K = °C + 273.15.
Therefore, the temperature in Kelvin is:
T = 11 °C + 273.15 = 284.15 K.
Step 2: Convert the given pressure from mm Hg to atm.
To convert mm Hg to atm, we use the conversion factor: 1 atm = 760 mm Hg.
Therefore, the pressure in atm is:
P = 754.5 mm Hg / 760 = 0.9938 atm.
Step 3: Use the ideal gas law to calculate the molar mass.
The ideal gas law is given by: PV = nRT, where:
P = pressure (in atm),
V = volume (in liters),
n = number of moles,
R = ideal gas constant (0.0821 L.atm/mol.K),
T = temperature (in Kelvin).
Rearranging the equation, we have: n = PV / RT.
Step 4: Calculate the number of moles using the given data.
n = (0.9938 atm) * (1 L) / (0.0821 L.atm/mol.K * 284.15 K)
= 0.0460 mol.
Step 5: Calculate the molar mass.
The molar mass (M) is calculated by dividing the mass of the gas by the number of moles.
M = mass / moles.
Given that the density of the gas is 2.875 g/L, we can calculate the mass of the gas in one liter:
Mass = density * volume.
Mass = (2.875 g/L) * (1 L) = 2.875 g.
Therefore, the molar mass is:
M = 2.875 g / 0.0460 mol = 62.5 g/mol.
Step 6: Determine the molecular formula of the gas.
To find the molecular formula, we need to know the molar mass of each element in the gas. Chlorine (Cl) has a molar mass of approximately 35.5 g/mol, and oxygen (O) has a molar mass of approximately 16 g/mol.
Let's assume the molecular formula of the gas is ClaOb.
The molar mass of the gas would then be M = 35.5a + 16b.
Substituting the molar mass we calculated (M = 62.5 g/mol), we have:
62.5 = 35.5a + 16b.
Since there are no fractional values in the molecular formula, we can consider possible whole number values for a and b.
Checking for a = 1 and b = 1:
62.5 = 35.5(1) + 16(1) = 52.5 + 16 = 68.5.
This value is not equal to 62.5.
Checking for a = 2 and b = 1:
62.5 = 35.5(2) + 16(1) = 71 + 16 = 87.
This value is not equal to 62.5.
Checking for a = 1 and b = 2:
62.5 = 35.5(1) + 16(2) = 35.5 + 32 = 67.5.
This value is not equal to 62.5.
Checking for a = 2 and b = 2:
62.5 = 35.5(2) + 16(2) = 71 + 32 = 103.
This value is not equal to 62.5.
Therefore, there is no combination of a and b that satisfies the equation M = 62.5 g/mol using whole number values.
Based on this calculation, it seems that the given molecular formula assumption ClaOb is not appropriate for this gas. It is possible that the molecular formula is different, or there may be other factors that affect the density of the gas.