0.249 g of a diatomic element occupies a volume of 125mL at 120 degrees C and 2.00 atm. This element is? Please help. I'm lost.
To identify the diatomic element, we can use the ideal gas law, which states:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature
In order to find the diatomic element, we need to determine the number of moles of the gas using the given information.
Step 1: Convert the temperature to Kelvin
The ideal gas law requires temperature to be in Kelvin. To convert Celsius to Kelvin, we use the formula:
T(K) = T(°C) + 273.15
Given T(°C) = 120°C,
T(K) = 120°C + 273.15 = 393.15 K
Step 2: Convert the volume to liters
The ideal gas law requires the volume to be in liters. To convert milliliters to liters, we divide by 1000:
V(L) = V(mL) / 1000
Given V(mL) = 125 mL,
V(L) = 125 mL / 1000 = 0.125 L
Step 3: Calculate the number of moles (n)
Rearrange the ideal gas law equation to solve for the number of moles (n):
n = PV / RT
Given P = 2.00 atm, V = 0.125 L, R = 0.0821 L·atm/(K·mol), and T = 393.15 K, we can substitute these values into the equation:
n = (2.00 atm) * (0.125 L) / (0.0821 L·atm/(K·mol)) * (393.15 K)
n ≈ 0.01208 mol
Step 4: Determine the molar mass
We can now determine the molar mass of the diatomic element by dividing the mass by the moles:
Molar mass = mass / moles
Given mass = 0.249 g and moles ≈ 0.01208 mol, we can substitute these values into the equation:
Molar mass ≈ 0.249 g / 0.01208 mol
Molar mass ≈ 20.551 g/mol
By referring to the periodic table and finding an element with a molar mass of approximately 20.551 g/mol, we can identify the diatomic element. In this case, the element with a molar mass closest to 20.551 g/mol is oxygen (O). Thus, the diatomic element is oxygen (O).