To identify a diatomic gas (X2), a researcher carried out the following experiment: She weighed an empty 2.8-L bulb, then filled it with the gas at 1.20atm and 22.0 ∘C and weighed it again. The difference in mass was 3.9g . Identify the gas.
Use PV = nRT, substitute the conditions and solve for n = number of mols. Then n = grmas/molar mass. You know mols and grams, solve for molar mass. Look on the periodic table and identify the gas.
To identify the gas in this experiment, we need to consider a few key concepts related to the ideal gas law and molar mass calculations.
The ideal gas law states that the pressure (P), volume (V), and temperature (T) of an ideal gas are related by the equation PV = nRT, where n is the number of moles of the gas and R is the ideal gas constant.
In this case, the researcher filled a 2.8-L bulb with the gas at a pressure of 1.20 atm and a temperature of 22.0 °C. They then weighed the bulb and found a difference in mass of 3.9 g. By comparing the initial and final weights of the bulb, we can determine the mass of the gas that was added.
To find the number of moles of gas, we'll need to convert the pressure, volume, and temperature to the appropriate units and use the ideal gas law.
First, let's convert the temperature from Celsius to Kelvin by adding 273.15:
T = 22.0 °C + 273.15 = 295.15 K
Next, let's convert the pressure from atm to Pascals (Pa) since the ideal gas constant (R) is typically expressed in J/(mol·K) and the SI unit for pressure is Pa:
P = 1.20 atm × 101325 Pa/atm = 121590 Pa
Now we can rearrange the ideal gas law equation to solve for the number of moles (n):
n = PV / RT
Substituting the values we have:
n = (121590 Pa) × (2.8 L) / [(8.314 J/(mol·K)) × (295.15 K)]
Now we can calculate the number of moles of the gas.
Finally, to identify the gas, we need to calculate its molar mass. We can do this by dividing the difference in mass of the bulb by the number of moles of the gas.
Once we have the molar mass, we can compare it to known molar masses to identify the gas. Diatomic gases are typically elements that exist as two atoms bonded together, like oxygen (O2), nitrogen (N2), or hydrogen (H2).
By following this process and performing the necessary calculations, we can determine the identity of the gas.