Please I need a detailed explanation, am stuck doing this assignment, at what temperature in kelvin will co2 molecules have an rms speed equal to hydrogen at 20 Celsius?

To find the temperature in Kelvin at which CO2 molecules have an RMS (Root Mean Square) speed equal to hydrogen at 20 Celsius, we need to follow a few steps:

Step 1: Convert the Celsius temperature of hydrogen to Kelvin.
Step 2: Calculate the RMS speed of hydrogen at that temperature.
Step 3: Calculate the RMS speed of CO2 molecules.
Step 4: Equate the RMS speeds of hydrogen and CO2 to find the temperature of CO2 in Kelvin.

Let's go through each step in detail:

Step 1: Convert the Celsius temperature of hydrogen to Kelvin.
To convert Celsius to Kelvin, we use the equation:
Kelvin = Celsius + 273.15.

Given that the Celsius temperature of hydrogen is 20°C, we can convert it to Kelvin:
Kelvin = 20°C + 273.15 = 293.15 K.

Step 2: Calculate the RMS speed of hydrogen at 293.15 K.
The RMS speed formula for a gas molecule is:
Vrms = √(3RT / M),

where:
Vrms 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 kg/mol.

The molar mass of hydrogen (H2) is approximately 2 g/mol or 0.002 kg/mol.

Plugging in the values, we get:
Vrms_hydrogen = √(3 * 8.314 J/(mol·K) * 293.15 K / 0.002 kg/mol).

Calculating this will give us the RMS speed of hydrogen at 293.15 K.

Step 3: Calculate the RMS speed of CO2 molecules.
The molar mass of CO2 is approximately 44 g/mol or 0.044 kg/mol.

Using the same formula as before, the RMS speed of CO2 is calculated as:
Vrms_CO2 = √(3 * 8.314 J/(mol·K) * T / 0.044 kg/mol).

Step 4: Equate the RMS speeds of hydrogen and CO2 to find the temperature of CO2 in Kelvin.
Now, we can set the two RMS speed formulas equal to each other and solve for T (temperature in Kelvin):
√(3 * 8.314 J/(mol·K) * T / 0.002 kg/mol) = √(3 * 8.314 J/(mol·K) * 293.15 K / 0.044 kg/mol).

Squaring both sides of the equation, we can simplify and solve for T:
3 * 8.314 J/(mol·K) * T / 0.002 kg/mol = 3 * 8.314 J/(mol·K) * 293.15 K / 0.044 kg/mol.

Canceling out common terms and solving for T, we find:
T = (0.002 / 0.044) * (293.15 K) = 133.409 K.

Therefore, at a temperature of approximately 133.409 Kelvin, the RMS speed of CO2 molecules will be equal to the RMS speed of hydrogen at 20 Celsius.

To find the temperature in Kelvin at which carbon dioxide (CO2) molecules have an RMS (Root Mean Square) speed equal to hydrogen (H2) molecules at 20 degrees Celsius, we can follow these steps:

Step 1: Convert the temperature of 20 degrees Celsius to Kelvin.
The formula to convert Celsius to Kelvin is: K = °C + 273.15

Given that the temperature is 20 degrees Celsius, we can calculate it as follows:
T(CO2) = 20 + 273.15
T(CO2) = 293.15 Kelvin

Step 2: Calculate the RMS speed for both CO2 and H2.
The RMS speed of a gas can be determined using the following equation:

Vrms = √(3RT / M)

Where:
Vrms is the RMS speed
R is the Universal Gas Constant (8.314 J/(mol·K))
T is the temperature in Kelvin
M is the molar mass of the gas in kg/mol

Step 3: Calculate the molar mass of CO2 and H2.
The molar mass of CO2 is calculated by adding up the atomic masses of carbon (C) and two oxygen (O) atoms:
M(CO2) = 12.01 g/mol + (16.00 g/mol * 2)
M(CO2) = 44.01 g/mol

The molar mass of H2 is obtained by adding up the atomic masses of two hydrogen (H) atoms:
M(H2) = 1.008 g/mol * 2
M(H2) = 2.016 g/mol

Step 4: Calculate the RMS speeds for CO2 and H2.
Using the equation mentioned in Step 2, we can now calculate the RMS speeds for both CO2 and H2:

Vrms(CO2) = √(3 * 8.314 * 293.15 / 0.04401) (using the molar mass of CO2)
Vrms(H2) = √(3 * 8.314 * 293.15 / 0.002016) (using the molar mass of H2)

Step 5: Compare the RMS speeds.
Compare the calculated RMS speeds for CO2 and H2. Find the temperature at which Vrms(CO2) is equal to Vrms(H2).

If the calculated RMS speeds are equal, then the temperatures at which they occur will also be equal.