Calculate the rms speed of gaseous I2 molecules at 23°C and 1.00 atm.
What is the rms speed of gaseous I2 at 23°C and 1.60 atm?
rms = sqrt(3RT/M) = sqrt(3*8.314*296/M). Plug in M for molar mass I2 and solve for rms velocity. Post your work if you get stuck.
To calculate the rms (root mean square) speed of gaseous I2 molecules at 23°C and a given pressure, we can use the following formula:
rms speed = sqrt((3 * k * T) / m)
where:
k = Boltzmann constant (1.38 * 10^-23 J/K)
T = temperature in Kelvin (23°C + 273.15 = 296.15 K)
m = molar mass of I2 (2 * atomic mass of I = 2 * 126.90 g/mol)
Using this formula, let's calculate the rms speed at 23°C and 1.00 atm:
rms speed = sqrt((3 * 1.38 * 10^-23 J/K * 296.15 K) / (2 * 126.90 g/mol))
Calculating this expression, we find that the rms speed at 23°C and 1.00 atm is approximately 362.25 m/s.
Now, let's calculate the rms speed at 23°C and 1.60 atm:
rms speed = sqrt((3 * 1.38 * 10^-23 J/K * 296.15 K) / (2 * 126.90 g/mol))
Calculating this expression, we find that the rms speed at 23°C and 1.60 atm is approximately 408.23 m/s.
To calculate the root mean square (rms) speed of gaseous I2 molecules, we can use the following formula:
v = √((3RT) / (M))
Where:
- v is the rms speed of the molecules,
- R is the gas constant (8.31 J/(mol·K)),
- T is the temperature in Kelvin,
- M is the molar mass of I2.
First, let's convert the given temperature of 23°C to Kelvin:
T = 23°C + 273.15 = 296.15 K
Next, we need to find the molar mass of I2. The molar mass of iodine (I) is approximately 126.9 g/mol. Since we have two iodine atoms in I2, the molar mass of I2 will be 2 * 126.9 g/mol = 253.8 g/mol.
Now we can substitute these values into the formula to calculate the rms speed at 1.00 atm:
v = √((3 * 8.31 J/(mol·K) * 296.15 K) / (253.8 g/mol))
Calculating this expression gives us the rms speed at 1.00 atm.
To calculate the rms speed of gaseous I2 molecules at a different pressure (1.60 atm), we need to note that the rms speed is directly proportional to the square root of temperature and inversely proportional to the square root of molar mass. Hence, at constant temperature, the rms speed is independent of pressure. Therefore, the rms speed of gaseous I2 at 23°C and 1.60 atm will be the same as at 1.00 atm.
Thus, the rms speed of gaseous I2 at 23°C and 1.60 atm is the same as the rms speed at 23°C and 1.00 atm that we calculated earlier.