'Imagine there is a tank of unknown gas that contains 53.31% carbon, 11.18% hydrogen, and 35.51% oxygen by mass. At 35.0 °C and 0.455 bar, 2.00 L of the gas has a mass of 3.20 g. Using this information, answer the following questions. a.) What is the empirical formula of the gas?. b.) how many moles of gas are in the tank?. c) What is the molecular formula of the gas?'
To find the empirical formula of the gas, we need to determine the simplest whole number ratio of the atoms present in the compound. We can do this by converting the mass percentages of each element into moles and dividing by the smallest number of moles obtained to obtain the ratio.
a) Calculation of the empirical formula of the unknown gas:
1. Convert the mass percentage of each element into grams.
Mass of carbon = 53.31% x 3.20 g = 1.703 g
Mass of hydrogen = 11.18% x 3.20 g = 0.358 g
Mass of oxygen = 35.51% x 3.20 g = 1.139 g
2. Convert the mass of each element into moles using their atomic masses:
Moles of carbon = 1.703 g / atomic mass of carbon
Moles of hydrogen = 0.358 g / atomic mass of hydrogen
Moles of oxygen = 1.139 g / atomic mass of oxygen
3. Divide the number of moles obtained by the smallest number of moles to obtain the simplest ratio.
Let's assume the smallest number of moles is the moles of hydrogen.
Ratio of carbon to hydrogen = Moles of carbon / Moles of hydrogen
Ratio of oxygen to hydrogen = Moles of oxygen / Moles of hydrogen
By finding the simplest whole number ratio of the three elements, we can determine the empirical formula of the gas.
b) To calculate the number of moles of gas in the tank, we can use the ideal gas law:
PV = nRT
Where:
P = pressure (in atm or bar)
V = volume (in liters)
n = number of moles
R = ideal gas constant (0.0821 L·atm/(K·mol) or 0.0831 L·bar/(K·mol))
T = temperature (in Kelvin)
In this case, we are given the pressure, volume, and temperature. By rearranging the equation, we can solve for the number of moles (n):
n = PV / RT
Substitute the given values into the equation to find the number of moles.
c) To determine the molecular formula of the gas, we need additional information about the molar mass of the compound. With the empirical formula obtained in part a), we can find the molecular formula by finding the molar mass of the compound. This can be done by multiplying the empirical formula's subscripts by a factor ("x") that gives the desired molar mass.