What is the average speed in m/s of O2 molecules in a tank at 445 K?
v = √((3RT) / (M))
Where:
v is the RMS speed,
R is the ideal gas constant (8.314 J/(mol·K)),
T is the temperature in Kelvin,
M is the molar mass of the gas.
In this case, the temperature is 445 K and the molar mass of O2 is 32 g/mol. We need to convert the molar mass to kg/mol, which is 0.032 kg/mol. Now, we can substitute the values into the formula:
v = √((3 * 8.314 * 445) / 0.032)
Simplifying the equation: v = √((9943.98) / (0.032)) v = √(310,748.125)
Calculating the square root: v ≈ 556.8 m/s
Explanation:
To calculate the average speed of O2 molecules in a tank at 445 K, we use the root mean square (RMS) speed formula. The formula takes into account the temperature and molar mass of the gas. In this case, the temperature is 445 K and the molar mass of O2 is 32 g/mol.
First, we convert the molar mass of O2 from grams per mole to kilograms per mole by dividing by 1000. This gives us a molar mass of 0.032 kg/mol. Next, we substitute the values of the ideal gas constant (8.314 J/(mol·K)), temperature (445 K), and molar mass (0.032 kg/mol) into the RMS speed formula.
After simplifying the equation and calculating the square root, we find that the average speed of O2 molecules in the tank at 445 K is approximately 556.8 m/s.
This calculation helps us understand the kinetic behavior of gas molecules at a given temperature. By knowing the average speed, we can make predictions about the movement and interactions of O2 molecules in the tank.