An unknown diatomic gas has a density of 1.428 g/L at STP. What is the identity of the gas? (Enter the formula of the gas. Omit states-of-matter from your answer.)
1 mol occupies 22.4 L so
how much will 22.4 L weigh if 1 L weighs 1.428 g?
To determine the identity of an unknown diatomic gas, we need to use the gas laws and the molar mass of each possible gas to find the one that matches the given density at STP (standard temperature and pressure).
Step 1: Determine the molar mass of each diatomic gas.
- The molar mass of a gas is the mass of one mole of that gas.
- The most common diatomic gases are oxygen (O2), nitrogen (N2), hydrogen (H2), chlorine (Cl2), bromine (Br2), and iodine (I2).
The molar mass of O2 = 2 * atomic mass of O = 2 * 16.00 g/mol = 32.00 g/mol
The molar mass of N2 = 2 * atomic mass of N = 2 * 14.01 g/mol = 28.02 g/mol
The molar mass of H2 = 2 * atomic mass of H = 2 * 1.01 g/mol = 2.02 g/mol
The molar mass of Cl2 = 2 * atomic mass of Cl = 2 * 35.45 g/mol = 70.90 g/mol
The molar mass of Br2 = 2 * atomic mass of Br = 2 * 79.90 g/mol = 159.80 g/mol
The molar mass of I2 = 2 * atomic mass of I = 2 * 126.90 g/mol = 253.80 g/mol
Step 2: Convert the given density to the units of g/mol.
- We know that density (d) = mass (m) / volume (V).
- At STP, 1 mole of any gas occupies 22.4 L. Therefore, the density can be calculated as:
density (d) = molar mass (M) / molar volume (V) = M / 22.4
Given:
density (d) = 1.428 g/L
Step 3: Calculate the molar mass for each gas using the given density.
- For each gas, divide the given density by 22.4 L/mol to obtain the molar mass.
For O2, molar mass = d * V = 1.428 g/L * 22.4 L/mol = 31.97 g/mol (rounded)
For N2, molar mass = d * V = 1.428 g/L * 22.4 L/mol = 31.97 g/mol (rounded)
For H2, molar mass = d * V = 1.428 g/L * 22.4 L/mol = 31.97 g/mol (rounded)
For Cl2, molar mass = d * V = 1.428 g/L * 22.4 L/mol = 31.97 g/mol (rounded)
For Br2, molar mass = d * V = 1.428 g/L * 22.4 L/mol = 31.97 g/mol (rounded)
For I2, molar mass = d * V = 1.428 g/L * 22.4 L/mol = 31.97 g/mol (rounded)
Step 4: Compare the calculated molar mass with the given values.
- The given density of 1.428 g/L corresponds to a molar mass of 31.97 g/mol.
- Comparing this value with the calculated molar mass for each gas, we find that it matches the molar mass of O2.
Therefore, the identity of the gas is O2 (oxygen).
To determine the identity of the gas, we need to use its density and the information about STP (Standard Temperature and Pressure).
STP is defined as a temperature of 0°C (273.15 K) and a pressure of 1 atmosphere (atm).
The density of a gas is related to its molar mass and molar volume by the ideal gas law:
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.
At STP, the molar volume of any gas is 22.414 L/mol. Therefore, we can rewrite the equation as:
P(22.414 L/mol) = M(molar mass)RT
From the given information, the density of the gas is 1.428 g/L. This means that for every liter of the gas, there is 1.428 grams of it.
To convert this to moles, we need to divide the given density by the molar mass.
1.428 g/L ÷ molar mass(g/mol) = 1.428 mol/L
Now we can substitute this value into the ideal gas law equation:
(1 atm)(22.414 L/mol) = (1.428 mol/L)(0.0821 L·atm/mol·K)(273.15 K)
Simplifying the equation, we find:
22.414 = 0.38242(273.15)
22.414 = 104.32839
Since this equation is not true, there must be a mistake in the calculation.
Please review the given information and the calculations to ensure accuracy.