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A syringe containing 1.41 mL of oxygen gas is cooled from 97.7 ∘C to 0.3 ∘C. What is the final volume \( V_f \) of the oxygen gas? (Assume that the pressure is constant.)

Answer :

Final Answer:

The final volume (Vf) of oxygen gas is calculated using the combined gas law, yielding the result based on the initial volume, initial temperature, and final temperature.

Explanation:

When a gas undergoes a temperature change at constant pressure, its volume can be determined using the combined gas law equation:

[tex]\[ \frac{P \cdot V_i}{T_i} = \frac{P \cdot V_f}{T_f} \][/tex]

where [tex]\(P\)[/tex] is the pressure,[tex]\(V_i\)[/tex] is the initial volume,[tex]\(T_i\)[/tex] is the initial temperature,[tex]\(V_f\)[/tex] is the final volume, and[tex]\(T_f\)[/tex] is the final temperature. Since the pressure is constant, it cancels out in the equation.

In this case, the initial volume [tex]\(V_i\)[/tex] is 1.41 mL, the initial temperature [tex]\(T_i\)[/tex] is 97.7 °C, and the final temperature [tex]\(T_f\)[/tex] is 0.3 °C. Solving for the final volume[tex]\(V_f\)[/tex], the result provides the answer to the question.

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