if the rms speed of NH3 molecules is found to be 0.510 km/s what is the temperature (in Celcius)?
can someone solve this using the formula
c=((2.55*R*T)/M)^1/2
c is the speed
r is 8.314 constant
M is the molar mass of NH3 17.031
btw i know the answer is -96 degrees C from the back of the book but i just wanna know how to get this answer
Here is what I would do.
u = sqrt(3RT/M)
u^2 = 3RT/M
510^2*M = 3RT
T = 510^2*M/3R
T = 510^2*0.01703/3*8.314
M is in kg
T = 177.59 K - 273.15 = -95.56
which rounds to -96 C.
I don't know where your 2.55 came from.
To solve for the temperature using the given formula c = ((2.55 * R * T) / M)^(1/2), you can follow these steps:
1. Rearrange the formula to solve for T (temperature):
c^2 = (2.55 * R * T) / M
Multiply both sides by M:
c^2 * M = 2.55 * R * T
Divide both sides by (2.55 * R):
(c^2 * M) / (2.55 * R) = T
2. Plug in the given values:
c = 0.510 km/s = 0.510 * 1000 m/s = 510 m/s (convert km/s to m/s)
R = 8.314 J/(mol*K) (universal gas constant)
M = 17.031 g/mol = 17.031 / 1000 kg/mol (convert g/mol to kg/mol)
3. Calculate the temperature:
T = (c^2 * M) / (2.55 * R)
T = (510^2 * (17.031 / 1000)) / (2.55 * 8.314)
Calculating the above expression will give you the temperature in Kelvin (K). To convert it to Celsius (°C), simply subtract 273.15 from the temperature in Kelvin.