### Gas Law Problems: Calculate the Unknown Parameter**Instructions**: This question has multiple parts. Work all the parts to get the most points. A gas sample is under an initial set of conditions (i) and is then changed to a final set of conditions (f). Use the combined gas law to calculate the unknown final parameter for this gas sample.#### Problem (a)- **Initial Conditions (i):** \( P_i = 3.90 \text{ atm} \) \( V_i = 3.00 \text{ L} \) \( T_i = 310. \text{ K} \) - **Final Conditions (f):** \( P_f = ? \text{ atm} \) \( V_f = 6.90 \text{ L} \) \( T_f = 470. \text{ K} \) Use the equation:\[ P_i V_i / T_i = P_f V_f / T_f \]to solve for \( P_f \):\[ P_f = \_\_\_\_\_\_ \text{ atm} \]#### Problem (b)- **Initial Conditions (i):** \( P_i = 4.37 \text{ atm} \) \( V_i = 1.82 \text{ L} \) \( T_i = 289 \text{ K} \) - **Final Conditions (f):** \( P_f = 2.01 \text{ atm} \) \( V_f = ? \text{ L} \) \( T_f = 370. \text{ K} \) Use the equation:\[ P_i V_i / T_i = P_f V_f / T_f \]to solve for \( V_f \):\[ V_f = \_\_\_\_\_\_ \text{ L} \]**Explanation**:- \( P \) represents pressure- \( V \) represents volume- \( T \) represents temperature- Subscript \( i \) refers to initial conditions- Subscript \( f \) refers to final conditionsBy understanding and applying the Combined Gas Law, we can determine unknown variables given a set of initial and final conditions of a gas sample. ### Example Problem: Ideal Gas Law ApplicationGiven the following initial and final states of an ideal gas, calculate the unknown final temperature.**Initial Conditions:**- Initial Pressure, \( P_i \): 7.71 atm- Initial Volume, \( V_i \): 8.05 L- Initial Temperature, \( T_i \): 590. K**Final Conditions:**- Final Pressure, \( P_f \): 3.10 atm- Final Volume, \( V_f \): 7.00 L- Final Temperature, \( T_f \): ? KCalculate the final temperature \( T_f \).\[ T_f = \, \boxed{ \ \ } \, \text{K} \] ### Explanation:To solve this problem, we can use the Ideal Gas Law's combined form:\[ \frac{P_i \cdot V_i}{T_i} = \frac{P_f \cdot V_f}{T_f} \]Rearrenging to solve for \( T_f \):\[ T_f = \frac{P_f \cdot V_f \cdot T_i}{P_i \cdot V_i} \]Substitute the values:\[ T_f = \frac{(3.10 \, \text{atm}) \cdot (7.00 \, \text{L}) \cdot (590. \, \text{K})}{(7.71 \, \text{atm}) \cdot (8.05 \, \text{L})} \]Calculate \( T_f \):\[ T_f = \boxed{K} \]

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A gas sample is under an initial set of conditions (i) and is then changed to a final set of conditions (f). Use the combined gas law to calculate the unknown final parameter for this gas sample. P 3.90 atm V 3.00 L T 310. K P, ? atm V, 6.90 L T 470. K

A gas sample is under an initial set of conditions (i) and is then changed to a final set of conditions (f). Use the combined gas law to calculate the unknown final parameter for this gas sample. P 3.90 atm V 3.00 L T 310. K P, ? atm V, 6.90 L T 470. K

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

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