Maths for A Level Chemistry - updated edition

Example If Q = mc Δ T , ϐind Q if m = 100 g, c = 4.18 J g −1  K −1 and Δ T =6K. Answer Q = mc Δ T Q = 100 × 4.18 × 6 Q = 2508 J If the unknown quantity is not the subject of the equation, then it is necessary to manipulate the equation. There are two ways of doing this: 1 Substitute the numbers into the equation and then manipulate. 2 Manipulate the equation to make the unknown quantity the subject and then substitute the numbers in. The following example shows the two methods. Example The ideal gas equation is pV = nRT . Find the value of p if n = 5, R = 8.31, V = 3 and T = 298. Answer Method 1 Substituting the numbers into the equation and then manipulating. pV = nRT p × 3 = 5 × 8.31 × 298 p = 5 × 8.31 × 298 3 = 4127.3 = 4130 (3 s.f.) Method 2 Manipulating the equation to make the unknown quantity the subject and then substituting the numbers in. pV = nRT p = nRT V = 5 × 8.31 × 298 3 = 4127.3 = 4130 (3 s.f.) 3.5 Logarithms What are logarithms? Look at the following 10 3 = 1000. This says that 10 to the power of 3 is equal to 1000. In the above example the 10 is called the base and the 3 is called the logarithm of 1000 to the base 10. We write 3 = log 10 1000. Pointer Always write out the equation you are going to use before substituting the numbers. Pointer In maths we do not always attach units to numbers. In chemistry, we nearly always have to consider units. This equation finds heat energy, so Q is measured in Joules. You need to know the context of the question in order to know what unit to use. Pointer As we only have to give the value of the pressure, we do not have to include any units. Mathematics for Chemistry 36