OF THE FOLLOWING SUBSTANCES, WHICH HAS THE LARGEST AVERAGE SPEED AT 25DEGREES. CO, NH3,H2,N2?
To determine which of the following substances has the largest average speed at 25 degrees Celsius (°C) - CO, NH3, H2, or N2 - we need to consider the root mean square (RMS) speed of the gas molecules.
The RMS speed of gas molecules is given by the equation:
v_rms = √(3RT / M)
Where:
- v_rms is the root mean square speed
- R is the ideal gas constant
- T is the temperature in Kelvin (K)
- M is the molar mass of the gas in kilograms per mole (kg/mol)
First, let's convert 25°C to Kelvin by adding 273.15:
T = 25°C + 273.15 = 298.15 K
Next, let's calculate the RMS speed for each gas by using their respective molar masses:
CO:
- Molar Mass (M) = 28.010 g/mol = 0.02801 kg/mol
- v_rms = √(3 * R * T / M) = √(3 * 8.314 J/(mol·K) * 298.15 K / 0.02801 kg/mol)
NH3:
- Molar Mass (M) = 17.031 g/mol = 0.017031 kg/mol
- v_rms = √(3 * R * T / M) = √(3 * 8.314 J/(mol·K) * 298.15 K / 0.017031 kg/mol)
H2:
- Molar Mass (M) = 2.016 g/mol = 0.002016 kg/mol
- v_rms = √(3 * R * T / M) = √(3 * 8.314 J/(mol·K) * 298.15 K / 0.002016 kg/mol)
N2:
- Molar Mass (M) = 28.013 g/mol = 0.028013 kg/mol
- v_rms = √(3 * R * T / M) = √(3 * 8.314 J/(mol·K) * 298.15 K / 0.028013 kg/mol)
By calculating the above expressions, we can find the RMS speed for each gas. The gas with the largest RMS speed will have the highest average speed.