At \(T(K)\), the rms velocity of methane is \(x \, {ms}^{-1}\). What is the kinetic energy (in J) of 8 g of methane at the same temperature
(Assume methane as an ideal gas)
1. Molar mass of methane (CH\(_4\)): * Molar mass = 12 (C) + 4(1) (H) = 16 g/mol = 0.016 kg/mol
2. Number of moles (n) of 8 g methane: n = mass / molar mass = 8 g / 16 g/mol = 0.5 moles
3. Relationship between rms velocity (x) and temperature (T): \(x = \sqrt{\frac{3RT}{M}}\)
Squaring both sides: \(x^2 = \frac{3RT}{M}\)
Rearranging for RT: \(RT = \frac{Mx^2}{3}\)
4. Kinetic energy (KE) of n moles of an ideal gas: KE = \(\frac{3}{2} nRT\)
5. Substitute the value of RT: KE = \(\frac{3}{2} n \left(\frac{Mx^2}{3}\right)\)
KE = \(\frac{1}{2} nMx^2\)
6. Substitute the values of n and M: KE = \(\frac{1}{2} \times 0.5 \, {mol} \times 0.016 \, {kg/mol} \times x^2\)
KE = \(0.004 \, {kg} \times x^2\)
KE = \(4 \times 10^{-3}x^2 \, {J}\)
Therefore, the kinetic energy of 8 g of methane at the same temperature is \(4 \times 10^{-3}x^2\) J.
Final Answer:
\(4 \times 10^{-3}x^2\) J.
Amino acids are represented by the following general structure:
Find out the pair in which amino acid is correctly matched with its group R:
Sucrose is a disaccharide of which of the following?
In which of the following the polymer is correctly matched with the catalyst used for its preparation?
I. Teflon - Persulphate
II. Low density polythene - Triethyl aluminium and titanium tetrachloride
III. Terylene - Zinc acetate/antimony trioxide
Two statements are given below
Statement I: Benzanamine can be prepared from phthalimide.
Statement II: Benzanamine is less basic than phenyl methanamine.
What are X and Z in the following reaction sequence?
What is Y in the following reaction sequence?
Observe the following set of reactions:
Correct statement regarding Y and B is:
What is X in the following reaction?