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Year 11 DP Chemistry Rob Slider

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Units Volume (V) SI unit: m 3 1m 3 = 1000 dm 3 = 1000L 1dm 3 = 1000cm 3 = 1000mL Volume (V) SI unit: m 3 1m 3 = 1000 dm 3 = 1000L 1dm 3 = 1000cm 3 = 1000mL Pressure (P) SI unit: Pa (pascal) atm (atmosphere) – the pressure acting on an object on Earth (standard pressure) 1atm = x 10 5 Pa 1kPa = 10 3 Pa 1atm = kPa Pressure (P) SI unit: Pa (pascal) atm (atmosphere) – the pressure acting on an object on Earth (standard pressure) 1atm = x 10 5 Pa 1kPa = 10 3 Pa 1atm = kPa Temperature (T) SI unit: K (Kelvin) K = 0 C C = K Absolute zero = 0K or C F.P. (water) = 273K or 0 0 C Temperature (T) SI unit: K (Kelvin) K = 0 C C = K Absolute zero = 0K or C F.P. (water) = 273K or 0 0 C

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Avogadros Hypothesis Law of Combining Gas Volumes The volume of gases taking part in a chemical reaction show simple whole number ratios to one another when those volumes are measured at the same temperature (T) and pressure (P) Law of Combining Gas Volumes The volume of gases taking part in a chemical reaction show simple whole number ratios to one another when those volumes are measured at the same temperature (T) and pressure (P) Avogadros Law When gases are at the same T & P, the same volume of any gas has the same amount of particles (moles) Avogadros Law When gases are at the same T & P, the same volume of any gas has the same amount of particles (moles) Practice Problem The molar and volume ratios of the following reaction are 2:1:2 since the reactants and products are gases. 2H 2 (g) + O 2 (g) -----> 2H 2 O(g) So, if there is 50mL of hydrogen gas, what are the volumes of oxygen gas and water vapour? 50mL of hydrogen gas would react with 50 x ½ = 25mL oxygen gas to produce 50mL of water vapour Practice Problem The molar and volume ratios of the following reaction are 2:1:2 since the reactants and products are gases. 2H 2 (g) + O 2 (g) -----> 2H 2 O(g) So, if there is 50mL of hydrogen gas, what are the volumes of oxygen gas and water vapour? 50mL of hydrogen gas would react with 50 x ½ = 25mL oxygen gas to produce 50mL of water vapour Example The molar ratio of the following reaction to produce ammonia gas is 1:3:2. N 2 (g) + 3H 2 (g) -----> 2NH 3 (g) Since all the reactants and products are gases, the mole ratio is the same as the ratio of the volumes of gases. So, 10mL of nitrogen gas reacts with 10 x 3 = 30mL of hydrogen gas to produce 10 x 2 = 20mL ammonia gas Example The molar ratio of the following reaction to produce ammonia gas is 1:3:2. N 2 (g) + 3H 2 (g) -----> 2NH 3 (g) Since all the reactants and products are gases, the mole ratio is the same as the ratio of the volumes of gases. So, 10mL of nitrogen gas reacts with 10 x 3 = 30mL of hydrogen gas to produce 10 x 2 = 20mL ammonia gas Note all of the reactants/products are gases Molar Volume of a Gas: At stp, 1 mole of any gas occupies 22.4dm 3 (stp is 273K and 101.3kPa)

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Exercises 1 1. Find the volume occupied by 8g of oxygen gas at STP. 2. How many cm 3 are there, at STP, in 1.72 g of phosphorous pentoxide (P 2 O 5 )? 3. What is the mass of 3.2 dm 3 of nitrogen gas measured at STP? 4. Find the mass of 275 cm 3 of phosphorous trichloride gas measured at STP. 5.6 dm cm g 1.69 g

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Boyles Law (P vs V) At constant temperature: Volume of a given quantity of gas is inversely proportional to pressure: V= 1 / P (E.g. if the volume of a gas is doubled, its pressure is halved.) OR The product of a gass volume and its pressure is a constant : PV = constant, PV = k At constant temperature: Volume of a given quantity of gas is inversely proportional to pressure: V= 1 / P (E.g. if the volume of a gas is doubled, its pressure is halved.) OR The product of a gass volume and its pressure is a constant : PV = constant, PV = k So, at constant temperature for a given quantity of gas : P i V i = P f V f where, P i and V i are the initial pressure and volume, P f and V f are the final pressure and volume. Note: pressures and volumes must be in the same units of measurement on each side. So, at constant temperature for a given quantity of gas : P i V i = P f V f where, P i and V i are the initial pressure and volume, P f and V f are the final pressure and volume. Note: pressures and volumes must be in the same units of measurement on each side. Ideal vs. Real gases All gases approximate Boyle's Law at high temperatures and low pressures. Ideal Gas - a hypothetical gas which obeys Boyle's Law at all temperatures and pressures Real Gas - approaches Boyle's Law behaviour as the temperature is raised or the pressure lowered. Ideal vs. Real gases All gases approximate Boyle's Law at high temperatures and low pressures. Ideal Gas - a hypothetical gas which obeys Boyle's Law at all temperatures and pressures Real Gas - approaches Boyle's Law behaviour as the temperature is raised or the pressure lowered.

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Boyles Law – inversely proportional Note how the volume changes in relation to the pressure exerted on a gas. At a given temperature, this relationship is predictable for an ideal gas. Twice the pressure (P2) = half the volume (V2)

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Boyles Law - Graph P vs V gives a parabolic shape V vs 1/P gives a linear shape

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Exercises 2 1. A sample of 200 cm 3 of a gas has a pressure of 1.00 atm. The pressure is increased to 1.10 atm at a constant temperature. Find the new volume of the gas mL of a gas is compressed to 135 mL with no change in temperature. If the original pressure was 1.05 x 10 5 Pa, what is the new pressure? dm 3 of gas was originally at a pressure of 1.20 atm. Under constant temperature conditions, what pressure in kPa would be needed to change the volume to 2.50 dm 3 ? 182 cm x 10 5 Pa 131 kPa

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Charles Law (T vs V) At constant pressure, Volume of a given quantity of gas is directly proportional to the absolute temperature : Vα T (in Kelvin) (E.g. if the temperature (K) is doubled, the volume of gas is also doubled.) OR The ratio of its volume and the absolute temperature is a constant : V / T = constant, V / T = k At constant pressure, Volume of a given quantity of gas is directly proportional to the absolute temperature : Vα T (in Kelvin) (E.g. if the temperature (K) is doubled, the volume of gas is also doubled.) OR The ratio of its volume and the absolute temperature is a constant : V / T = constant, V / T = k V i /T i = V f /T f So, at constant pressure: V i /T i = V f /T f where, T i and V i are the initial temperature and volume, T f and V f are the final temperature and volume. Note: T i and T f must be in Kelvin NOT Celsius. (temperature in Kelvin = temperature in Celsius + 273) (approximately) V i /T i = V f /T f So, at constant pressure: V i /T i = V f /T f where, T i and V i are the initial temperature and volume, T f and V f are the final temperature and volume. Note: T i and T f must be in Kelvin NOT Celsius. (temperature in Kelvin = temperature in Celsius + 273) (approximately) Ideal vs. Real gases All gases approximate Charles' Law at high temperatures and low pressures. Well above its condensation point, the volume of a real gas decreases linearly as it is cooled at constant pressure. However, as the gas approaches the condensation point, the decrease in volume slows down. At condensation, the gas turns to a liquid and, therefore, does not obey Charles Law Absolute zero (OK) is the temperature where the volume of a gas would theoretically be zero if it did not condense. Ideal vs. Real gases All gases approximate Charles' Law at high temperatures and low pressures. Well above its condensation point, the volume of a real gas decreases linearly as it is cooled at constant pressure. However, as the gas approaches the condensation point, the decrease in volume slows down. At condensation, the gas turns to a liquid and, therefore, does not obey Charles Law Absolute zero (OK) is the temperature where the volume of a gas would theoretically be zero if it did not condense.

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Note how the volume changes in relation to temperature with constant pressure applied At a given pressure, the pressure is directly proportional to the volume. (As temperature goes up, so does the pressure) Try this: fill a balloon with air, then put it in the freezer. What happened? How does this demonstrate Charles Law? Increase the temperature and the volume goes up Same pressure

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Charles Law - Graph Volume is directly proportional to absolute temperature (linear) Extrapolate this relationship back to absolute zero where the volume of a gas is theoretically zero and all molecular motion stops. Is this possible?

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Exercises 3 1. A given sample of gas has a volume of 5.0 m 3 at a temperature of C. What volume would it occupy at 300 K assuming the pressure remains constant? cm 3 of a gas is heated from 0 0 C to 91 0 C. Assuming no pressure change, find the new volume. 3. When heated under constant pressure, the volume of a gas increased from 2.42 dm 3 to 2.67 dm 3. If the initial temperature was 19 0 C, find the final temperature in 0 C. 6.0 m cm C

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Gay-Lussacs Law (P vs T) At constant volume, Pressure of a given quantity of gas is directly proportional to its temperature OR the ratio of pressure and temperature is equal to a constant p/T = k (a constant) At constant volume, Pressure of a given quantity of gas is directly proportional to its temperature OR the ratio of pressure and temperature is equal to a constant p/T = k (a constant) p i /T i = p f /T f So, at constant volume: p i /T i = p f /T f where, p i and T i are the initial pressure and temperature, p f and T f are the final pressure and temperature. Note: pressures and temperature (Kelvin) must be in the same units of measurement on each side. p i /T i = p f /T f So, at constant volume: p i /T i = p f /T f where, p i and T i are the initial pressure and temperature, p f and T f are the final pressure and temperature. Note: pressures and temperature (Kelvin) must be in the same units of measurement on each side.

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Gay-Lussacs Law Note the effect that increased temperature has on the pressure of the container which is at constant volume. An increase in temperature leads to increased pressure

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Gay-Lussac - Graph Note how pressure increases as the temperature increases as the average kinetic energy of the particles exerts more force on a container of constant volume

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How does this photo relate to Gay-Lussacs Law??

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Exercises 4 1. At a given temperature of 7 0 C, a sample of gas has a pressure of 1.40 atm. If it is heated to 320 K, while the volume stays constant, what would the new pressure be? 2. The pressure of a gas is reduced from kPa to 97.5 kPa. If the volume does not change, calculate the final temperature in Celsius if the initial temperature was 15 0 C. 3. A sample of gas has an initial temperature of 10 0 C. If the pressure is doubled, find the resulting temperature in Celsius assuming constant volume atm 1 0 C C

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Combined Gas Law If we combine all three individual gas laws into one, we can show how pressure, temperature and volume are related in one equation. p i V i = p f V f T i T f p i V i = p f V f T i T f This equation can be used if there is more than one variable changing at once. Temperature must be in Kelvin. Pressure and volume can be in any unit as long as they are the same on both sides of the equation.

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Exercises 5 1. A gas sample of 32.0 cm 3 has a pressure of 1.05 atm and a temperature of C. What would be the volume of the gas at a pressure of 1.12 atm and a temperature of C? 2. At 0.75 atm and C a gas has a volume of 100 cm 3. Find the volume at STP. 3. A sample of gas occupies m 3 at 1.14 atm and 9 0 C. Calculate the volume at STP. 4. When measured at kPa and C, some gas has a volume of 232 mL. What would be the volume in litres at STP? 28 cm 3 82 cm m L

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Ideal Gas Law An Ideal Gas (perfect gas) is one which obeys Boyle's Law, Charles' Law and G-Ls Law exactly. An Ideal Gas obeys the Ideal Gas Law (General gas equation): PV = nRT where, P=pressure, V=volume, n=moles of gas, T=temperature, R=the gas constant (dependent on the units of pressure, temperature and volume) R = J K -1 mol -1 P is in (Pa), V is in (m 3 ), T is in (K) (note: J = m 3 Pa) R = L atm K -1 mol -1 P (atm), V (L), T (K) An Ideal Gas (perfect gas) is one which obeys Boyle's Law, Charles' Law and G-Ls Law exactly. An Ideal Gas obeys the Ideal Gas Law (General gas equation): PV = nRT where, P=pressure, V=volume, n=moles of gas, T=temperature, R=the gas constant (dependent on the units of pressure, temperature and volume) R = J K -1 mol -1 P is in (Pa), V is in (m 3 ), T is in (K) (note: J = m 3 Pa) R = L atm K -1 mol -1 P (atm), V (L), T (K)

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Presumptions – Is any gas ideal? Presumptions of an Ideal Gas according to Kinetic Theory of Gases: Presumptions of an Ideal Gas according to Kinetic Theory of Gases: Gases consist of molecules which are in continuous random motion Gases consist of molecules which are in continuous random motion The volume of the molecules present is negligible relative to the total volume occupied by the gas The volume of the molecules present is negligible relative to the total volume occupied by the gas Intermolecular forces are negligible Intermolecular forces are negligible Pressure is due to the gas molecules colliding with the walls of the container Pressure is due to the gas molecules colliding with the walls of the container Real Gases deviate from Ideal Gas Behaviour because Real Gases deviate from Ideal Gas Behaviour because at low temperatures the gas molecules have less kinetic energy (move around less) so they do attract each other at low temperatures the gas molecules have less kinetic energy (move around less) so they do attract each other at high pressures the gas molecules are forced closer together so that the volume of the gas molecules becomes significant compared to the volume the gas occupies at high pressures the gas molecules are forced closer together so that the volume of the gas molecules becomes significant compared to the volume the gas occupies The Overall Presumption The Overall Presumption Under ordinary conditions, deviations from Ideal Gas behaviour are so slight that they can be neglected. A gas which deviates from Ideal Gas behaviour is called a non-ideal gas. Under ordinary conditions, deviations from Ideal Gas behaviour are so slight that they can be neglected. A gas which deviates from Ideal Gas behaviour is called a non-ideal gas.

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Gas Law Summary Charles Law V i /T i = V f /T f Charles Law V i /T i = V f /T f Boyles Law P i V i = P f V f Boyles Law P i V i = P f V f Gay-Lussacs Law p i /T i = p f /T f Gay-Lussacs Law p i /T i = p f /T f Ideal Gas Law pV = nRT Ideal Gas Law pV = nRT

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Exercises moles of a gas at 25 0 C and 1.15 atm occupies what volume? 2. Magnesium reacts with hydrochloric acid to produce hydrogen gas and magnesium chloride a) What volume of gas is evolved at 273 K and 1 atm pressure when g of Mg reacts with 27.3 cm 3 of 1.25 mol dm -3 hydrochloric acid. b) Calculate the volume occupied by the hydrogen gas evolved if it is collected at 22 0 C and 1.12 atm pressure. c) If the actual volume of hydrogen collected was 342 cm3, what is the percentage yield?

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