Calculate the rms speed of Br2 molecules at 23 °C and 1.00 atm. What is the rms speed of Br2 at 23 °C and 1.50 atm?
To calculate the root mean square (RMS) speed of Br2 molecules, we can use the following formula:
RMS speed = √(3RT/M)
where:
R = Ideal Gas Constant = 8.314 J/(mol·K)
T = Temperature in Kelvin
M = Molar mass of Br2 in kg/mol
First, let's calculate the RMS speed of Br2 molecules at 23 °C and 1.00 atm.
1. Converting temperature to Kelvin:
T = 23 °C + 273.15 = 296.15 K
2. Calculating the molar mass of Br2:
M = 2 × (molar mass of Br) = 2 × (79.904 g/mol) = 159.808 g/mol = 0.159808 kg/mol
3. Plugging the values into the equation:
RMS speed = √(3 × 8.314 J/(mol·K) × 296.15 K / 0.159808 kg/mol)
= √(7474.64 J/mol / 0.159808 kg/mol)
= √(46826.78 m^2/s^2)
≈ 216.32 m/s
Therefore, the RMS speed of Br2 molecules at 23 °C and 1.00 atm is approximately 216.32 m/s.
To calculate the RMS speed of Br2 molecules at 23 °C and 1.50 atm, we don't need to repeat the previous steps. We just need to substitute the new pressure value into the formula:
RMS speed = √(3 × 8.314 J/(mol·K) × 296.15 K / 0.159808 kg/mol)
≈ √(46826.78 m^2/s^2) × (1.50 / 1.00)
≈ 1.50 × 216.32 m/s
≈ 324.48 m/s
Therefore, the RMS speed of Br2 molecules at 23 °C and 1.50 atm is approximately 324.48 m/s.
To calculate the root-mean-square (rms) speed of a gas molecule, we can use the following formula:
v(rms) = √((3RT) / M)
where:
v(rms) is the rms speed of the gas molecule,
R is the gas constant (8.314 J/(mol·K)),
T is the temperature in Kelvin (K), and
M is the molar mass of the gas molecule (in kg/mol).
Let's start by calculating the rms speed of Br2 molecules at 23 °C and 1.00 atm:
1. Convert 23 °C to Kelvin:
T = 23 + 273.15 = 296.15 K
2. Determine the molar mass of Br2:
The molar mass of Br2 is 79.90 g/mol. This needs to be converted to kg/mol:
M = 79.90 g/mol / 1000 g/kg = 0.0799 kg/mol
3. Substitute the values into the formula:
v(rms) = √((3 * R * T) / M)
v(rms) = √((3 * 8.314 J/(mol·K) * 296.15 K) / 0.0799 kg/mol)
Calculate the square root and simplify the expression to find the rms speed.
Now, let's calculate the rms speed of Br2 at 23 °C and 1.50 atm:
Follow the same steps as before, but this time use 1.50 atm instead of 1.00 atm. The temperature remains the same (23 °C), so you don't need to recalculate T or M.
4. Substitute the new pressure value into the formula:
v(rms) = √((3 * 8.314 J/(mol·K) * 296.15 K) / 0.0799 kg/mol)
Calculate the square root and simplify the expression to find the rms speed at the new pressure of 1.50 atm.
change temp to Kelvins.
the equation is simple: Vrms= sqrt (3RT/massBr2) get R in the units of Kelvin, mass of bromine in kg, and temp in kelvins)