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Understanding the Ideal Gas Law: PV = nRT Explained

The Ideal Gas Law, expressed as PV = nRT, defines the relationship between pressure (P), volume (V), temperature (T), and the amount of gas in moles (n). It quantitatively describes the behavior of gases under various conditions, making it essential for calculations in chemistry and physics. By manipulating the variables, one can predict how a gas will respond to changes in its environment, providing valuable insights for scientific applications and real-world scenarios.

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Understanding the Ideal Gas Law: PV = nRT Explained

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  1. The Ideal Gas Law

    PV = nRT
  2. Definition The ideal gas law is the mathematical relationship among: Pressure (P) Volume (V) Temperature (T) Amount of the Gas in Moles (n) The law quantitatively describes the behavior of a gas sample for any combination of conditions: If you know three of the conditions, you can solve for the fourth. PV = nRT
  3. Units of Measurement Volume must always be measured in liters (L). 1L = 1000mL = 0.001kL Amount of the gas must always be measured in moles (mol). If amount is given in grams, you must do a gram to mole conversion! Temperature must always be measured in Kelvin (K). K = ˚C + 273 ˚C = K - 273 Pressure must always be measured in atmospheres (atm). 1 atm= 760 mmHg = 760 torr= 1.013 x 105 Pa = 101.3 kPa
  4. Standard Temperature and Pressure (STP) Standard temperature is 273 K. Standard pressure is 1 atm. At STP, 1 mole of any ideal gas occupies 22.4 L.
  5. The Ideal Gas Constant Represented as R in the ideal gas law. R is a constant value that never changes. The value for R is derived from the standard volume (22.4L) of 1 mole of a gas at STP. PV = nRT can be arranged as R = PV/nT R = (1 atm)(22.4 L)/(1 mol)(273 K) = 0.0821 L•atm/mol•K PV = nRT
  6. Solving Ideal Gas Law Problems What is the pressure exerted by a 0.500 mol sample of nitrogen gas in a 10.0L container at 25˚C? 1. Determine given values and unknown. n= 0.500 mol, V = 10.0 L, T = 25˚C , R = 0.0821 L•atm/mol•K P = ? 2. Convert given values into proper units. K = 25˚C + 273 = 298 K 3. Rearrange equation to solve for unknown. Plug in given values to solve for unknown. P = nRT/V P = (o.500 mol)(0.0821 L•atm/mol•K)(298 K) / 10.0 L P = 1.22 atm
  7. Solving Ideal Gas Law Problems What is the volume of an 8.00g sample of oxygen gas at 293 K and 0.974 atm? 1. Determine given values and unknown. n= 8.00g, T = 293 K , P = 0.974 atm, R = 0.0821 L•atm/mol•K V= ? 2. Convert given values into proper units. 8.oo g O2 x (1 mol O2 / 32.00 g O2 ) = 0.250 mol O2 3. Rearrange equation to solve for unknown. Plug in given values to solve for unknown. V = nRT/P V= (o.250 mol)(0.0821 L•atm/mol•K)(293 K) / 0.974 atm V = 6.17 L
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