Helium gas occupies a volume of 0.04m^3 at a pressure of 2 x 10^5 Nm^-2 and temperature 300K. Calculate the mass of the helium and root mean square speed of its molecules. [ Relative molecular mass of helium = 4, molar gas constant = 8.31 J mol-1 K-1]

Following are the differences betweenr real gases and ideal gases:

Value of R is a constant for all gases while value of r is a variable for all gases but a constant for a specific gas.

Explanation:

Starting with the Ideal gas equation,PV = nRT.

R in the above equation stands for Universal Gas Constant whose value is a constant 8.314 J/mol-K for all gases.

However, when we put n = M/m where M represents total mass of gas present and m the molar mass of the gas.

The value of R/m = r or r = R/m is defined as the specific gas constant for a gas. Clearly, r is a...

The speed of molecules follows directly from measuring the pressure and density-you don’t need to know the size of molecules. In standard kinetic theory collisions with other molecules have always been ignored because the molecules were tiny. Though theyaren't. So the molecules are not going in straight line. Thus it takes time for the smell to spread in the room.

At Initial state

p_i = 1atm

T₀=-173^oc =100k

v_i=v

Finally

P_f= 2 atm

T_f = ?

V_f= v(constant)

By ideal gas law

PV = nRT

V = T/P = constant

T_i/p_i= T_f/p_f

T_f = T_i*P_f/p_i

=100*2/1

= 200k = -73^oc

A kilogram of hydrogen is having more molecules.

Explanation:
For hydrogen that value is 1.008. For oxygen it’s 16.00. That means however many times you can divide the mass by its molar mass, So for example 1000g (1kg) / 1.008 is approximately992 moles of hydrogen. And 1000g/16.00 is 62.5 moles of Oxygen. Now to put it all together, one mole is equal to 6.02x10^23 molecules so obviously since there are more moles of hydrogen, you would have a significantly larger amount of hydrogen.

At absolute zero the molecular motion of gases ceases to zero because, at this point volume of gases is said to zero.

Now at T = 0 K, kinetic energy=0

Therefore, the molecular motion is also zero.

The ideal gas law fails at low temperature and high-pressure becausethe volume occupied by the gas is quite small, so the inter-molecular distance between the molecules decreases.

The unit of the Universal Gas Constant, also known as the ideal gas constant, is joules per mole per kelvin (J/mol·K). Its physical meaning is that it relates the physical properties of gases, such as pressure, volume, and temperature, through the ideal gas law equation: PV = nRT.