87. At what temperature would CO2 molecules have an rms speed equal to H2 molecules 25 degrees C?

First I got the rms of H2 to be 1927.3
by taking u= sq root (3*8.31*298)/(.002

Then I tried to find the temp of CO2 by using 1927.3 sq root .044/ sq root (3*8.31) and I got 81.0 K.

Can someone tell me what I did wrong?

Well, it seems like you've been having a gassy situation with your calculations! But don't worry, Clown Bot is here to provide some comedic relief.

It looks like you've made a little mistake in your equation when trying to find the temperature of CO2. Instead of using the mass of CO2 (0.044 kg/mol), you should actually be using the molar mass (0.044 kg/mol) divided by the molecular weight of CO2 (44.01 g/mol).

So, let's do some recalculations and find out the correct temperature. The equation should be:

u = sqrt((3 * R * T) / M)

where:
u = root mean square speed,
R = ideal gas constant (8.31 J/(mol*K)),
T = temperature (in Kelvin),
M = molar mass (in kg/mol).

For H2:
M_H2 = 2.02 g/mol = 0.00202 kg/mol

So, rearranging the equation to solve for T_H2:

T_H2 = (u^2 * M_H2) / (3 * R)

Plug in the values:
T_H2 = [(1927.3 m/s)^2 * 0.00202 kg/mol] / (3 * 8.31 J/(mol*K))
T_H2 = 1875541.7534 K

Now, let's find the temperature for CO2:

M_CO2 = 44.01 g/mol = 0.04401 kg/mol

Rearranging the equation for CO2:

T_CO2 = (u^2 * M_CO2) / (3 * R)

Plug in the values:
T_CO2 = [(1927.3 m/s)^2 * 0.04401 kg/mol] / (3 * 8.31 J/(mol*K))
T_CO2 = 5242.0185 K

So, the temperature at which CO2 molecules would have an rms speed equal to H2 molecules at 25 degrees C is approximately 5242.0 Kelvin. Make sure to double-check the calculations, as my jokes are much more reliable than my math skills!

To find the temperature at which CO2 molecules have an rms speed equal to H2 molecules at 25 degrees C, you need to use the formula for the root mean square (rms) speed of a gas molecule:

u = sqrt(3RT / M)

Where:
- u is the rms speed
- R is the gas constant (approximately 8.31 J/mol·K)
- T is the temperature in Kelvin
- M is the molar mass of the gas molecule

First, let's calculate the rms speed of H2 molecules at 25 degrees C.

Given:
- R = 8.31 J/mol·K
- T = 25 degrees C = 25 + 273.15 = 298.15 K
- M(H2) = 2 g/mol

Let's substitute these values into the formula:

u(H2) = sqrt(3 * 8.31 * 298.15 / 2)

Calculating this gives us:
u(H2) ≈ 1932 m/s (rounded to the nearest whole number)

Now let's find the temperature at which CO2 molecules would have the same rms speed.

Given:
- u(CO2) = u(H2) ≈ 1932 m/s
- M(CO2) = 44 g/mol

Rearranging the formula to solve for T, we have:

T = (u^2 * M) / (3 * R)

Substituting the known values:

T(CO2) = (1932^2 * 44) / (3 * 8.31)

Calculating this gives us:
T(CO2) ≈ 303 K (rounded to one decimal place)

So, at approximately 303 Kelvin (or 30 degrees Celsius), the CO2 molecules would have an rms speed equal to the rms speed of H2 molecules at 25 degrees Celsius.

It seems like you made a mistake when trying to find the temperature of CO2. Let's go through the correct calculation.

To find the temperature at which CO2 molecules have an rms speed equal to H2 molecules at 25 degrees Celsius (298 Kelvin), we can use the formula:

urms = sqrt(3 * k * T / m)

Where:
urms is the root mean square speed
k is the Boltzmann constant (8.31 J/mol-K)
T is the temperature in Kelvin
m is the molar mass of the molecule

First, you correctly calculated the root mean square speed of H2 molecules to be 1927.3 m/s:

urms_H2 = sqrt(3 * 8.31 * 298 / 0.002) = 1927.3 m/s

To find the temperature at which CO2 molecules have the same root mean square speed, we rearrange the formula:

T_CO2 = m_CO2 * urms_H2^2 / (3 * k)

The molar mass of CO2 is approximately 44 g/mol (0.044 kg/mol). Plugging in the values:

T_CO2 = 0.044 * (1927.3)^2 / (3 * 8.31) = 1094.15 K

So, at the same root mean square speed as H2 at 25 degrees Celsius, CO2 molecules would need to be at a temperature of approximately 1094.15 Kelvin.

Please let me know if you have any further questions!

You didn't show your work so we can't tell you where you went wrong. As a starter; however, I obtained closer to 1920 for urms for H2 (and I used 0.002016 for molar mass H2). Then I plugged in 0.04401 and the other numbers and obtained T = about 6505 K. Check me out on that.