When elemental sulfur,S8,is heated with AgF,a gas forms that contains only sulfur and fluorine. The following tests were done to
characterize this gaseous product.
*The density of the gas was found to be 0.807g/L at 152mmHg and 35 degrees celsius.
*When the gas reacts with water, all the fluorine is converted to aqueous HF. A 480-mL sample of the dry gas at 125 mmHg and 28 degrees celsius, when reacted with 80.0 mL of water, yielded a 0.080 M solution of HF. What is the empirical formula?
The empirical formula is SF4.
To find the empirical formula of the gas formed when elemental sulfur reacts with AgF, we need to analyze the given information.
1. Finding the molar mass of the gas:
Since we have the density of the gas and the conditions of temperature and pressure, we can use the ideal gas law to find the molar mass (M) of the gas.
PV = nRT
Where:
P = pressure = 152 mmHg
V = volume = 0.480 L
R = ideal gas constant = 0.0821 L·atm/(mol·K)
T = temperature = 35°C = 35+273 = 308 K
By rearranging the ideal gas law equation to solve for n, the number of moles, we get:
n = (PV) / (RT)
Substituting the given values:
n = (152 mmHg * 0.480 L) / (0.0821 L·atm/(mol·K) * 308 K)
Convert mmHg to atm:
n = (0.202 atm * 0.480 L) / (0.0821 L·atm/(mol·K) * 308 K)
n ≈ 0.0511 mol
To find the molar mass (M), we can divide the mass of the gas by the number of moles (n).
Mass = density * volume
Mass = 0.807 g/L * 0.480 L = 0.387 g
Molar mass (M) = Mass / n
Molar mass (M) = 0.387 g / 0.0511 mol ≈ 7.57 g/mol
2. Reacting the gas with water to form HF:
The gas reacts with water to produce HF. Using the given information, we can determine the moles of HF produced.
Given volume of gas = 0.480 L
Given pressure of gas = 125 mmHg
Given temperature of gas = 28°C = 28+273 = 301 K
Volume of water added = 80.0 mL = 0.080 L
Concentration of HF = 0.080 M
Using the ideal gas law, we can calculate the number of moles (n) of the gas:
n = (PV) / (RT)
Substituting the given values:
n = (125 mmHg * 0.480 L) / (0.0821 L·atm/(mol·K) * 301 K)
Convert mmHg to atm:
n = (0.164 atm * 0.480 L) / (0.0821 L·atm/(mol·K) * 301 K)
n ≈ 0.0331 mol
The moles of HF formed is equal to the moles of gas reacted because all the fluorine in the gas is converted to HF.
Concentration (M) = moles (n) / volume (V)
0.080 M = (0.0331 mol) / (0.080 L)
Solving for moles:
0.080 M * 0.080 L = (0.0331 mol) * V
0.0064 mol = 0.0331 mol * V
V ≈ 0.193 L
This means that the moles of HF formed is approximately 0.0331 mol.
3. Finding the empirical formula:
To determine the empirical formula, we need to find the ratio of sulfur (S) to fluorine (F) in the compound.
From the molecular weight (based on molar mass), we can calculate the number of moles of sulfur (nS) and fluorine (nF) in the compound.
nS = molar mass (M) / atomic mass of S = 7.57 g/mol / 32.06 g/mol = 0.236 mol
nF = 0.0331 mol - 0.236 mol = 0.033 mol
Now we can simplify the ratio of moles to the smallest whole numbers by dividing both moles by the smallest value (0.033 mol):
nS / smallest value = 0.236 mol / 0.033 mol ≈ 7
nF / smallest value = 0.033 mol / 0.033 mol = 1
Thus, the empirical formula is SF7.
To determine the empirical formula of the gaseous compound formed from the reaction between elemental sulfur (S8) and AgF, we can use the given information about the density of the gas and its reaction with water to calculate the molar mass of the compound.
1. Calculating the molar mass:
First, we need to calculate the molar mass of the compound using the density of the gas. The ideal gas law equation (PV = nRT) can be used to calculate the number of moles (n):
PV = nRT
Where:
P = pressure (152 mmHg, which we can convert to atm by dividing by 760)
V = volume (0.480 L)
n = number of moles
R = ideal gas constant (0.0821 L.atm/mol.K)
T = temperature (35 °C, which we can convert to Kelvin by adding 273.15)
Converting the Celsius temperature to Kelvin:
T(K) = T(°C) + 273.15
T(K) = 35 + 273.15
T(K) = 308.15 K
Now, we can substitute the values into the equation and solve for n:
(152/760) * 0.480 = n * 0.0821 * 308.15
n ≈ 0.0101 mol (moles of the gaseous compound)
To find the molar mass (M), we can divide the mass by the number of moles:
M = mass (g) / n (mol)
The given density is 0.807 g/L, so the mass of the gas can be calculated:
mass = density * volume
mass = 0.807 g/L * 0.480 L
mass ≈ 0.387 g
Now, substitute the values into the equation:
M = 0.387 g / 0.0101 mol
M ≈ 38.3 g/mol
2. Calculating moles of fluorine:
From the given information, when the gas reacts with water, all the fluorine is converted to aqueous HF. A 480 mL sample of the dry gas at 125 mmHg and 28 degrees Celsius, when reacted with 80.0 mL of water, yielded a 0.080 M solution of HF.
Using the equation moles = concentration * volume:
moles of HF = 0.080 M * (80.0 mL / 1000 mL/L)
moles of HF ≈ 0.0064 mol
Since all the fluorine (F) atoms in the compound are converted to HF, we can assume that the number of moles of F is equal to the number of moles of HF.
3. Determining the empirical formula:
Now that we have the number of moles of F, we can calculate the number of moles of S:
moles of S = moles of compound - moles of F
moles of S = 0.0101 mol - 0.0064 mol
moles of S ≈ 0.0037 mol
To find the empirical formula, we need to determine the ratio of moles of elements. Since the molar mass of sulfur is 32.06 g/mol and the molar mass of fluorine is 19.00 g/mol, we can calculate the ratio:
Moles of S / Moles of F = (0.0037 mol / 32.06 g/mol) / (0.0064 mol / 19.00 g/mol)
Moles of S / Moles of F ≈ 0.115
Since we want the smallest whole number ratio, we can multiply it by a suitable factor to obtain whole numbers. In this case, we can multiply by 13:
Moles of S / Moles of F ≈ 1.50
Therefore, the empirical formula for the gaseous compound formed from the reaction between elemental sulfur (S8) and AgF is approximately SF1.5. We can multiply all the subscripts by 2 to obtain the simplest whole-number ratio, giving us the empirical formula SF3.