An unknown gas at 130 celsius has a rms speed that is 0.50 that of the rms speed of N2 molecules at 50 degrees celsius. What is the molecular weight of unknown gas?

M = 613.8455 kg/mol

Explanation:

RMS velocity or root mean square velocity has a formula for particles:

RMS = (3*R*T/ M)^ (1/2)

Where R is the ideal gas constant = 8.314 (kg*m^2 / s^2)/ K*mol

T is the temperature in Kelvin

M is the mass of a mole of the gas in kilograms (kg)

1) Convert the temperature to Kelvin for the N2 particles

T = *C +273  

T = 50 + 273

T = 323 K

2) Find the molar mass of the particles in kg for N2

using the periodic table: Nitrogen (N) molar mass is 14.00667 g/mol

N2 molar mass = 2 * 14.00667 = 28.01334 g/mol

Convert to kg/mol using dimensional analysis and conversion factor of 1 kg = 1000 g

28.01334 g / mol * 1 kg / 1000 g = 0.02801334 kg/mol

4) find the RMS of N2

RMS = (3 * (8.314 (kg*m^2 / s^2)/K*mol) * (323K) / 0.02801334 kg/mol))^1/2

=536.2712 m/s

5)If we take 0.5 of N2 RMS or 1/2 we get: 268.1356 m/s for the RMS of the unknown gas

6) Rearrange the equation to solve for M

RMS=(3RT/M)^1/2

Solve for M

We know that a^(1/2) = sqrt(a)

sqrt(RMS) = (3RT/M)

sqrt(RMS) * M = 3RT

M = 3RT / sqrt(RMS)

5) Change the temperature to Kelvins

T = 130 +273 = 403 K

6) Plug the numbers in and solve for M

M = (3*(8.314 (kg*m^2 / s^2)/K*mol) * (403 K)) / sqrt(268.1356 m/s)

M = 613.8455 kg/mol

answer is: nuclear fusion produces elements that are heavier than helium.

nuclei combine to form a heavier nucleus, releasing energy.  

for example, fusion of hydrogen atoms at the sun.  

this fusion nuclear reaction is in the inner core of the sun and hydrogen (atomic number 1) is conveted into helium (atomic number 2).  

the inner core is the central region of the sun and all solar energy is produced in the core by nuclear fusion.