Gen Chem Exams

Ideal Gas Law Context

• The ideal gas law relates pressure, volume, temperature, and number of moles of a gas: ( PV = nRT ).
• ( P ) represents pressure, ( V ) is volume, ( n ) is the number of moles, ( R ) is the ideal gas constant, and ( T ) is temperature.

Given Conditions

• A mass of ( O_2 ) is 64 g.
• The volume ( V ) is 8.2 L.
• Pressure ( P ) is 760 Torr.

Gas Constant Values

• ( R ) can be expressed in different units:
  • Atm: ( 0.082 , L , atm/(K , mol) )
  • Joules: ( 8.314 , J/(K , mol) )

Calculation Steps

• First, calculate the number of moles ( n ) of ( O_2 ):
  • Molar mass of ( O_2 ) is approximately 32 g/mol.
  • Moles ( n = \frac{64 , g}{32 , g/mol} = 2 , mol ).

Pressure Conversion

• Convert 760 Torr to atm for consistency with ( R ):
  • ( 760 , Torr = 1 , atm ).

Possible Answer Choices

• Each option represents a calculation to find temperature from the ideal gas law:
  • A: ( \frac{(1)(8.2)}{(4)(8.314)} )
  • B: ( \frac{(1)(8.2)}{(2)(0.082)} )
  • C: ( \frac{(1)(2)(0.082)}{8.2} )
  • D: ( \frac{(1)(8.2)}{(2)(8.314)} )

Choosing the Correct Option

• Identify the correct option based on calculated values and units used in each calculation.
• Since ( n = 2 , mol ), ( P = 1 , atm ), and ( V = 8.2 , L ), recognize which formula aligns with the ideal gas law using ( R = 0.082 ) or ( R = 8.314 ) based on the atmospheric pressure conversion.

Oxide Formation and Mass Ratio

• Element X forms an oxide denoted as (X_2O_3).
• The mass ratio of X to oxygen (O) in the oxide is given as 0.50 g X per 1 g O.

Calculating Atomic Mass of X

• Calculate the mass ratio of X: (0.50 , \text{g X} / 1 , \text{g O}) implies the molar ratio in analysis.
• Molar mass of oxygen (O) is 16.0 amu; hence the mass of 3 moles of oxygen (from (O_3)) is (3 \times 16.0 , \text{amu} = 48.0 , \text{amu}).
• For (2) moles of X in (X_2O_3), the mass ratio helps determine the mass of X:
  • For (0.50 , \text{g X}), the corresponding moles can be determined relative to the molar mass of oxygen.

Density of Mass Contribution

• If the mass of (X) is (M) amu, then for (X_2O_3):
  • Total mass of (2) moles of X = (2M).
• Using the mass ratio in the context of total component mass:
  • ( (2M)/(3 \times 16.0 , \text{amu}) = 0.50 ) leads to solving for M.

Atomic Mass Options

• After calculations, the possible atomic masses of X are provided as:
  • A. 12.0 amu
  • B. 16.0 amu
  • C. 24.0 amu
  • D. 32.0 amu.
• Determine which mass aligns with the derived equations from the above data.

Conclusion

• Understanding mass ratios and molar relationships between elements is crucial for determining unknown atomic masses.

Test your knowledge of gas laws in chemistry with this quiz. You will need to calculate the temperature at which a specific amount of oxygen occupies a given volume under defined conditions. Each option presents a different formula for you to evaluate.