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Published byJoel Dower Modified over 2 years ago

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Problem Solving: Using Either P 1 V 1 T 1 P 2 V 2 T 2 = or PV = nRT

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1)A 2.00 L bottle containing only air is sealed at a temperature of 22°C and a pressure of atm. The bottle is placed in a freezer and allowed to cool to 3.0°C. What is the pressure in the bottle? Step 1:Decide which formula to use. P 1 V 1 T 1 P 2 V 2 T 2 = Step 2:Identify variables given & variable that is unknown. V is constant because bottle does not change. T 1 = 22 o CP 1 = atm T 2 = 3.0 o CP 2 = ? atm

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Step 3:Convert all temperatures to KELVIN & make sure pressure units are consistent. T 1 = = 295 KT 2 = = 276 K Step 4:Plug in all known values into equation = P Step 5:Solve for the Unknown (do the math!). (.982)(276) = 295 P 2 P 2 =.919 atm

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2) Hydrogen gas is collected by water displacement. Total volume collected is L at a temperature of 17°C and a pressure of mmHg. What volume of dry hydrogen gas is collected? Step 1:Decide which formula to use. P 1 V 1 T 1 = P 2 V 2 T 2 Step 2:Identify variables given & variable that is unknown. Total Volume = V 1 V 1 = L Temperature is constant. P 1 = mmHg V 2 = volume of dry hydrogen = ?? P 2 = must subtract water vapor 17 o C from P 1

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Step 3:Convert all temperatures to KELVIN & make sure pressure units are consistent. Not needed since temperature is constant. Step 4:Determine the water vapor pressure in atmospheres at 17 o C and subtract this value from P 1. T ( o C) P (mmHg) T ( o C) P (mmHg) P 2 = – 14.5 = mmHg Step 5:Plug in all known values into equation. (751.64)(.461) = (737.14) V 2 Step 6:Solve for the Unknown (do the math!). ( x.461) =0.470 L

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3) What pressure in atmospheres will 1.36 kg of N 2 O gas exert when it is compressed in a 25.0 L cylinder and is stored in an outdoor shed where the temperature can reach 59°C during the summer? Step 1:Decide which formula to use. PV = nRT Step 2:Identify variables given & variable that is unknown. Mass = 1.36 kg V = 25.0 L T = 59 o C P = ?? atm R = L-atm/K-mol

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1.36 kg N 2 O must be converted to moles using the molar mass of N 2 O Molar mass N 2 O: (2 x 14.01) = g/mol Step 3:Convert all temperatures to KELVIN & make sure pressure units are consistent. T = = 332 K Step 4:Convert mass to moles kg1000 g 1 kg 1 mol g =30.9 mol Step 5:Plug in all known values into equation. P (25.0) = (30.9)(.0821)(332) Step 6:Solve for the Unknown (do the math!). P = (30.9 x.0821 x 332) 25.0 P = 33.6 atm Make sure answer has unit of pressure required!!

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