An unknown diatomic gas has a density of 1.250 g/L at STP. What is the identity of the gas? (Enter the formula of the gas. Omit states-of-matter from your answer.)
Hmm, let me gas-pire what the answer could be. With a density of 1.250 g/L, at STP, we need to clown into the periodic table for some gaseous possibilities. Now, let me see... Ah! I have a gas-piration! How about we pop a joke with some Hydrogen gas? So, the formula of the unknown diatomic gas could be H2!
To determine the identity of the diatomic gas, we need to use the ideal gas law and the molar mass of different diatomic gases to find a match.
1. Start with 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.
2. Since the gas is at STP (Standard Temperature and Pressure), the pressure (P) and temperature (T) can be defined:
- STP pressure (P) = 1 atm (atmosphere)
- STP temperature (T) = 273.15 K (Kelvin)
3. Rearrange the ideal gas law equation to solve for the number of moles (n):
n = PV / RT
4. Plug in the given values:
- P = 1 atm
- V = 1.250 g/L
- R = 0.0821 L·atm/(mol·K)
- T = 273.15 K
n = (1 atm) * (1.250 g/L) / (0.0821 L·atm/(mol·K)) * (273.15 K)
5. Perform the calculations:
n = 0.04952 mol
6. Now, to find the identity of the gas, compare the molar mass of the unknown gas with the molar masses of different diatomic gases until we find a match.
Let's consider some common diatomic gases:
- Hydrogen (H2): Molar mass = 2 g/mol
- Oxygen (O2): Molar mass = 32 g/mol
- Nitrogen (N2): Molar mass = 28 g/mol
- Chlorine (Cl2): Molar mass = 71 g/mol
Divide the given mass (1.250 g) by the calculated number of moles (0.04952 mol) to find the molar mass:
Molar mass = (1.250 g) / (0.04952 mol) ≈ 25.255 g/mol
7. Comparing the calculated molar mass to the molar masses of different diatomic gases, we find that it is closest to the molar mass of Nitrogen (N2), which is 28 g/mol.
Therefore, the identity of the unknown diatomic gas is Nitrogen, N2.
To determine the identity of the unknown diatomic gas, we need to consider its molar mass and use the ideal gas equation at STP (Standard Temperature and Pressure) conditions.
1. Determine the molar mass of the gas:
The molar mass of a substance is the mass of one mole of that substance. In this case, since we are dealing with an unknown diatomic gas, we need to find the molar mass.
Given that the gas has a density of 1.250 g/L at STP, we can convert this value to the molar mass by using the molar volume at STP, which is 22.4 L.
Molar mass (g/mol) = Density (g/L) × Molar volume (L/mol)
Molar mass = 1.250 g/L × 22.4 L/mol
Calculate the molar mass using the given density value.
2. Identify the gas:
Once we have calculated the molar mass, we can compare it to the molar masses of known gases to determine the identity of the unknown gas. Each gas has a unique molar mass based on its molecular formula.
You can refer to a periodic table or a database of molar masses to find the gas that matches the calculated molar mass.
So, follow these steps to identify the gas:
1. Calculate the molar mass of the unknown gas using the given density value and the molar volume at STP.
2. Compare the calculated molar mass to known molar masses of diatomic gases to identify the gas.
Remember to omit the states-of-matter when entering the formula of the gas.
one mole of gas occupies 22.4 L at STP
the molar mass of the gas is ... 1.250 g/L * 22.4 L = ?
solve for the molar mass of the gas
... then find the atomic molar mass for the "di"atomic gas
... look up the gas in the periodic table
enter the diatomic formula