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**Problem Solving: Using Either**

The Gas Laws Problem Solving: Using Either P1V1 T1 P2V2 T2 or = PV = nRT

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Example Problems 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. P1V1 T1 P2V2 T2 = Step 2: Identify variables given & variable that is unknown. V is constant because bottle does not change. T1 = 22oC P1 = atm T2 = 3.0oC P2 = ? atm

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Step 3: Convert all temperatures to KELVIN & make sure pressure units are consistent . T1 = = 295 K T2 = = 276 K Step 4: Plug in all known values into equation. .982 295 P2 276 = Step 5: Solve for the Unknown (do the math!). (.982)(276) = 295 P2 P2 = 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. P1V1 T1 P2V2 T2 = Step 2: Identify variables given & variable that is unknown. Total Volume = V1 V1 = L Temperature is constant. P2 = must subtract water vapor 17oC from P1 P1 = mmHg V2 = volume of dry hydrogen = ??

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**T (oC) P (mmHg) P (mmHg) 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 17oC and subtract this value from P1. P2 = – = mmHg T (oC) P (mmHg) P (mmHg) 10 9.2 17 14.5 11 9.8 18 15.5 12 10.5 19 16.5 13 11.2 20 17.5 14 21 18.7 15 12.8 22 19.8 16 13.6 23 21.1 Step 5: Plug in all known values into equation. (751.64)(.461) = (737.14) V2 Step 6: Solve for the Unknown (do the math!). ( x .461) 737.14 = 0.470 L

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**3) What pressure in atmospheres will 1**

3) What pressure in atmospheres will 1.36 kg of N2O 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 = kg V = L T = 59oC P = ?? atm R = L-atm/K-mol

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**Make sure answer has unit of pressure required!!**

Step 3: Convert all temperatures to KELVIN & make sure pressure units are consistent . T = = K Step 4: Convert mass to moles. 1.36 kg N2O must be converted to moles using the molar mass of N2O Molar mass N2O: (2 x 14.01) = g/mol 1.36 kg 1000 g 1 mol = 30.9 mol g 1 kg Step 5: Plug in all known values into equation. Make sure answer has unit of pressure required!! P (25.0) = (30.9)(.0821)(332) Step 6: Solve for the Unknown (do the math!). P = (30.9 x x 332) 25.0 P = atm

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