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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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Mullis1 Gay Lussac’s law of combining volumes of gases When gases combine, they combine in simple whole number ratios. These simple numbers are the coefficients.

Mullis1 Gay Lussac’s law of combining volumes of gases When gases combine, they combine in simple whole number ratios. These simple numbers are the coefficients.

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