Problem 1
What is \(0.0006 \mathrm{m}\) in (a) \(\mathrm{mm},(\mathrm{b}) \mathrm{pm},(\mathrm{c}) \mathrm{cm},(\mathrm{d}) \mathrm{nm} ?\)
Problem 2
A typical \(\mathrm{C}=\mathrm{O}\) bond distance in an aldehyde is \(122 \mathrm{pm} .\) What is this in \(\mathrm{nm} ?\)
Problem 3
The relative molecular mass of \(\mathrm{NaCl}\) is 58.44 and its density is \(2.16 \mathrm{g} \mathrm{cm}^{-3} .\) What is the volume of \(1 \mathrm{mole}\) of \(\mathrm{NaCl}\) in \(\mathrm{m}^{3} ?\)
Problem 4
The equation \(E=h \nu\) relates the Planck constant \((h)\) to energy and frequency. Determine the SI units of the Planck constant.
Problem 5
Kinetic energy is given by the equation: \(E=\frac{1}{2} m v^{2}\) By going back to the base SI units, show that the units on the left- and right-hand sides of this equation are compatible.
Problem 6
Calculate the relative atomic mass of a sample of naturally occurring boron which contains \(19.9 \%\) \(^{10} \mathrm{B}\) and \(80.1 \%_{5}^{11} \mathrm{B} .\) Accurate masses of the isotopes to 3 sig. fig. are 10.0 and 11.0
Problem 7
The mass spectrum of molecular bromine shows three lines for the parent ion, \(\mathrm{Br}_{2}^{+} .\) The isotopes for bromine are \(_{35}^{79} \mathrm{Br}(50 \%)\) and \(_{35}^{81} \mathrm{Br}(50 \%) .\) Explain why there are three lines and predict their mass values and relative intensities. Predict what the mass spectrum of HBr would look like; isotopes of hydrogen are given in Section \(1.7 .\) (Ignore fragmentation; see Chapter \(10 .\)
Problem 8
Convert the volume of each of the following to conditions of standard temperature \((273 \mathrm{K})\) and pressure ( 1 bar \(=1.00 \times 10^{5} \mathrm{Pa}\) ) and give your answer in \(\mathrm{m}^{3}\) in each case: (a) \(30.0 \mathrm{cm}^{3}\) of \(\mathrm{CO}_{2}\) at \(290 \mathrm{K}\) and \(101325 \mathrm{Pa}(1 \mathrm{atm})\) (b) \(5.30 \mathrm{dm}^{3}\) of \(\mathrm{H}_{2}\) at \(298 \mathrm{K}\) and \(100 \mathrm{kPa}(1 \mathrm{bar})\) (c) \(0.300 \mathrm{m}^{3}\) of \(\mathrm{N}_{2}\) at \(263 \mathrm{K}\) and \(102 \mathrm{kPa}\) (d) \(222 \mathrm{m}^{3}\) of \(\mathrm{CH}_{4}\) at \(298 \mathrm{K}\) and \(200000 \mathrm{Pa}(2 \mathrm{bar})\)
Problem 9
The partial pressure of helium in a \(50.0 \mathrm{dm}^{3}\) gas mixture at \(285 \mathrm{K}\) and \(10^{5} \mathrm{Pa}\) is \(4.0 \times 10^{4} \mathrm{Pa} .\) How many moles of helium are present?
Problem 10
A \(20.0 \mathrm{dm}^{3}\) sample of gas at \(273 \mathrm{K}\) and 2.0 bar pressure contains 0.50 moles \(\mathrm{N}_{2}\) and 0.70 moles Ar. What is the partial pressure of each gas, and are there any other gases in the sample? (Volume of one mole of ideal gas at \(273 \mathrm{K}, 1.00 \times 10^{5} \mathrm{Pa}(1 \mathrm{bar})=\) \(\left.22.7 \mathrm{dm}^{3} .\right)\)
