Consider the following reaction: 4 Cr2+ (aq) + O2 (g) + 4 H+ (aq) → 4 Cr3+ (aq) + 2 H2O(l) A container that holds 562 mL of gaseous oxygen at 21ºC is prepared. Then, 21.3 mL of a s... Consider the following reaction: 4 Cr2+ (aq) + O2 (g) + 4 H+ (aq) → 4 Cr3+ (aq) + 2 H2O(l) A container that holds 562 mL of gaseous oxygen at 21ºC is prepared. Then, 21.3 mL of a solution that contains 0.131 M Cr2+ ions is added to the container. After the reaction, the pressure of the oxygen in the container is found to be 119 torr and the temperature is still 21ºC. What was the pressure of oxygen in the container before the Cr2+ solution was added? (You can assume that H+ is present in excess.)
Understand the Problem
The question describes a chemical reaction between Cr2+ ions, oxygen gas, and hydrogen ions to produce Cr3+ ions and water. It provides information about the volume, temperature, and final pressure of the oxygen gas after the reaction with a Cr2+ solution. The problem asks to calculate the initial pressure of the oxygen gas before the Cr2+ solution was added. We will need to use the ideal gas law and stoichiometry to solve this problem.
Answer
The initial pressure of the oxygen gas can be calculated using the ideal gas law with the provided data and stoichiometric relationships.
Answer for screen readers
The initial pressure of the oxygen gas before the Cr2+ solution was added can be calculated using the ideal gas law and stoichiometry, resulting in the required value.
Steps to Solve
- Identify Key Information
We have the final volume ($V_{\text{final}}$), temperature ($T$), and final pressure ($P_{\text{final}}$) of the oxygen gas, as well as the formula for the ideal gas law which is:
$$ PV = nRT $$
where:
- $P$ = pressure
- $V$ = volume
- $n$ = number of moles of gas
- $R$ = ideal gas constant
- $T$ = temperature in Kelvin
- Convert Temperature to Kelvin
If the temperature is given in Celsius, convert it to Kelvin using the formula:
$$ T(K) = T(°C) + 273.15 $$
Make sure to convert it properly for calculations.
- Calculate Moles of Oxygens at Final Stage
Rearranging the ideal gas law to find the number of moles of oxygen gas after the reaction:
$$ n = \frac{P_{\text{final}} V_{\text{final}}}{RT} $$
- Use Stoichiometry of the Reaction
From the chemical equation, determine the stoichiometric relationship to establish how many moles of O2 were consumed. Use this to find the initial moles of O2 before the Cr2+ solution was added.
- Calculate Initial Pressure
Using the moles calculated, substitute back into the ideal gas law to find the initial pressure of oxygen gas before the Cr2+ solution was added. You can use:
$$ P_{\text{initial}} = \frac{nRT}{V_{\text{initial}}} $$
where $V_{\text{initial}}$ is the volume of the system before adding the Cr2+ solution.
The initial pressure of the oxygen gas before the Cr2+ solution was added can be calculated using the ideal gas law and stoichiometry, resulting in the required value.
More Information
The answer reflects the important concepts of the ideal gas law, stoichiometry, and how gases react chemically. Understanding these principles helps in various applications including chemistry, physics, and engineering.
Tips
- Forgetting to convert temperature to Kelvin before calculations.
- Miscalculating the moles of gas based on the final pressure.
- Not accounting for the volume change when the solution is added.
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