# 246 chapter 13 quantitative aspects of chemical

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CHAPTER 13. QUANTITATIVE ASPECTS OF CHEMICAL CHANGE - GRADE 11 13.7 Important: The standard units used for this equation are P in Pa, V in m 3 and T in K. Remember also that 1000cm 3 = 1dm 3 and 1000dm 3 = 1m 3 . Worked Example 67: Ideal Gas Question: A sample of gas occupies a volume of 20 dm 3 , has a temperature of 280 K and has a pressure of 105 Pa. Calculate the number of moles of gas that are present in the sample. Answer Step 1 : Convert all values into SI units The only value that is not in SI units is volume. V = 0.02 m 3 . Step 2 : Write the equation for calculating the number of moles in a gas. We know that pV = nRT Therefore, n = pV RT Step 3 : Substitute values into the equation to calculate the number of moles of the gas. n = 105 × 0 . 02 8 . 31 × 280 = 2 . 1 2326 . 8 = 0 . 0009moles Exercise: Using the combined gas law 1. An enclosed gas has a volume of 300 cm 3 and a temperature of 300 K. The pressure of the gas is 50 kPa. Calculate the number of moles of gas that are present in the container. 2. What pressure will 3 mol gaseous nitrogen exert if it is pumped into a container that has a volume of 25 dm 3 at a temperature of 29 0 C? 3. The volume of air inside a tyre is 19 litres and the temperature is 290 K. You check the pressure of your tyres and find that the pressure is 190 kPa. How many moles of air are present in the tyre? 4. Compressed carbon dioxide is contained within a gas cylinder at a pressure of 700 kPa. The temperature of the gas in the cylinder is 310 K and the number of moles of gas is 13 moles carbon dioxide. What is the volume of the gas inside? 13.7 Molar concentrations in liquids A typical solution is made by dissolving some solid substance in a liquid. The amount of substance that is dissolved in a given volume of liquid is known as the concentration of the liquid. Mathematically, concentration (C) is defined as moles of solute (n) per unit volume (V) of solution. 247
13.7 CHAPTER 13. QUANTITATIVE ASPECTS OF CHEMICAL CHANGE - GRADE 11 C = n V For this equation, the units for volume are dm 3 . Therefore, the unit of concentration is mol. dm 3 . When concentration is expressed in mol. dm 3 it is known as the molarity (M) of the solution. Molarity is the most common expression for concentration. Definition: Concentration Concentration is a measure of the amount of solute that is dissolved in a given volume of liquid. It is measured in mol.dm 3 . Another term that is used for concentration is molarity (M) Worked Example 68: Concentration Calculations 1 Question: If 3.5 g of sodium hydroxide (NaOH) is dissolved in 2.5 dm 3 of water, what is the concentration of the solution in mol. dm 3 ? Answer Step 1 : Convert the mass of NaOH into moles n = m M = 3 . 5 40 = 0 . 0875 mol Step 2 : Calculate the concentration of the solution. C = n V = 0 . 0875 2 . 5 = 0 . 035 The concentration of the solution is 0.035 mol.dm 3 or 0.035 M Worked Example 69: Concentration Calculations 2 Question: You have a 1 dm 3 container in which to prepare a solution of potassium permanganate (KMnO 4 ). What mass of KMnO 4 is needed to make a solution with a concentration of 0.2 M?

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