Chapter 22: Problem 14
The speeds of a group of ten molecules are \(2.0,3.0,4.0, \ldots\), \(11 \mathrm{~km} / \mathrm{s}\). ( \(a\) ) Find the average speed of the group. (b) Calculate the root-mean-square speed of the group.
Chapter 22: Problem 14
The speeds of a group of ten molecules are \(2.0,3.0,4.0, \ldots\), \(11 \mathrm{~km} / \mathrm{s}\). ( \(a\) ) Find the average speed of the group. (b) Calculate the root-mean-square speed of the group.
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Get started for freeCalculate the root-mean-square speed of smoke particles of mass \(5.2 \times 10^{-14} \mathrm{~g}\) in air at \(14^{\circ} \mathrm{C}\) and \(1.07\) atm pressure.
(a) Find the number of molecules in \(1.00 \mathrm{~m}^{3}\) of air at \(20.0^{\circ} \mathrm{C}\) and at a pressure of \(1.00 \mathrm{~atm} .(b)\) What is the mass of this volume of air? Assume that \(75 \%\) of the molecules are nitrogen \(\left(\mathrm{N}_{2}\right)\) and \(25 \%\) are oxygen \(\left(\mathrm{O}_{2}\right)\).
(a) Consider \(1.00 \mathrm{~mol}\) of an ideal gas at \(285 \mathrm{~K}\) and \(1.00 \mathrm{~atm}\) pressure. Imagine that the molecules are for the most part evenly spaced at the centers of identical cubes. Using Avogadro's constant and taking the diameter of a molecule to be \(3.00 \times 10^{-8} \mathrm{~cm}\), find the length of an edge of such a cube and calculate the ratio of this length to the diameter of a molecule. The edge length is an estimate of the distance between molecules in the gas. (b) Now consider a mole of water having a volume of \(18 \mathrm{~cm}^{3}\). Again imagine the molecules to be evenly spaced at the centers of identical cubes and repeat the calculation in \((a)\).
Show that, for atoms of mass \(m\) emerging as a beam from a small opening in an oven of temperature \(T\), the most probable speed is \(v_{\mathrm{p}}=\sqrt{3 \mathrm{kT} / \mathrm{m}}\).
The mass of the \(\mathrm{H}_{2}\) molecule is \(3.3 \times 10^{-24} \mathrm{~g}\). If \(1.6 \times 10^{23}\) hydrogen molecules per second strike \(2.0 \mathrm{~cm}^{2}\) of wall at an angle of \(55^{\circ}\) with the normal when moving with a speed of \(1.0 \times 10^{5} \mathrm{~cm} / \mathrm{s}\), what pressure do they exert on the wall?
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