To identify a diatomic gas (), a researcher carried out the following experiment: She weighed an empty 2.4- bulb, then filled it with the gas at 1.70 and 28.0 and weighed it again. The difference in mass was 4.7 . Identify the gas.
To identify the diatomic gas, we can use the ideal gas law equation: PV = nRT.
Given:
- Initial mass of the bulb (empty): m = 2.4 g
- Pressure of the gas: P = 1.70 atm
- Volume of the bulb: V = 28.0 L
- Difference in mass after filling: Δm = 4.7 g
Step 1: Convert the mass difference to moles.
To do this, we need the molar mass of the gas. Let's assume the molar mass of the gas is M.
Number of moles (n) = Δm / M
Step 2: Calculate the number of moles using the ideal gas law.
Using the ideal gas law equation PV = nRT, we can rearrange it to find the number of moles (n):
n = PV / RT
Where:
R is the ideal gas constant (0.0821 L·atm/(K·mol))
T is the temperature in Kelvin (K)
Step 3: Identify the gas using its molar mass.
To identify the gas, we can compare its molar mass (M) with the known molar masses of diatomic gases.
If you provide the temperature (T) during the experiment, we can proceed with calculating the molar mass (M) and identifying the gas.
To identify the gas, we need to use the information given and apply the ideal gas equation. The formula for the ideal gas equation is:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles of gas
R = ideal gas constant
T = temperature
Given information:
Initial mass of the bulb (empty) = 2.4 g
Mass of the gas-filled bulb = (initial mass + difference in mass) = (2.4 g + 4.7 g) = 7.1 g
Pressure of the gas-filled bulb = 1.70 atm
Temperature of the gas-filled bulb = 28.0 °C
First, we need to convert the temperature from Celsius to Kelvin:
T(K) = T(°C) + 273.15
T(K) = 28.0 °C + 273.15 = 301.15 K
Next, we can rearrange the ideal gas equation to solve for the number of moles (n):
n = (PV) / (RT)
Substituting the given values:
P = 1.70 atm
V = unknown
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = 301.15 K
Now we can determine the volume (V):
V = (nRT) / P
But we still need to determine the number of moles (n). To do that, we can use the difference in mass (m) and the molecular weight (M) of the gas.
The formula for the number of moles (n) is:
n = m / M
Substituting the given values:
m = 4.7 g (difference in mass)
To find the molecular weight (M) of the gas, we need to know its identity. Since the gas is mentioned to be diatomic, we know it's a molecule composed of two atoms.
Some common diatomic gases are nitrogen (N2), oxygen (O2), hydrogen (H2), chlorine (Cl2), etc.
We can calculate the molecular weight (M) for each possible diatomic gas using the periodic table and compare it to the calculated number of moles (n). The gas that matches the value of n is the correct one.
For example, let's take nitrogen (N2) as a candidate. The molecular weight of nitrogen (N2) is approximately 28 g/mol.
n = m / M
n = 4.7 g / 28 g/mol
n ≈ 0.168 mol
Now, substitute the calculated value of n back into the equation to determine the volume (V):
V = (nRT) / P
V = (0.168 mol) * (0.0821 L·atm/(mol·K)) * (301.15 K) / (1.70 atm)
Simplifying the expression will give you the value of V, which is the volume of the gas in liters. Once again, the volume is specific to the gas being identified.
Repeat this process for each candidate gas to determine the volume, and the gas that corresponds to the given volume is the answer.