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... 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 reaction between Cr2+ ions, oxygen gas, and hydrogen ions to form Cr3+ ions and water. We are given the volume and temperature of the oxygen gas, as well as the volume and concentration of the Cr2+ solution. After the reaction the pressure is measured. The goal is to determine the initial pressure of the oxygen gas before adding Cr2+.
Answer
The initial pressure of the oxygen gas can be calculated using the formula: $$ P_{initial} = \frac{n_{O2\, initially} \cdot R \cdot T}{V_{O2}} $$
Answer for screen readers
The initial pressure of the oxygen gas can be calculated using:
$$ P_{initial} = \frac{n_{O2, initially} \cdot R \cdot T}{V_{O2}} $$
Steps to Solve
- Identify Given Information
We have the following information:
- Volume of oxygen gas (V_O2)
- Temperature (T)
- Volume of Cr2+ solution (V_Cr2+)
- Concentration of Cr2+ solution (C_Cr2+)
- Measured pressure after the reaction (P_final)
- Convert Cr2+ concentration to moles
Calculate the initial number of moles of Cr2+ using the concentration and volume of the solution. The formula is:
$$ n_{Cr2+} = C_{Cr2+} \cdot V_{Cr2+} $$
Where:
- $C_{Cr2+}$ is the concentration of Cr2+ in mol/L
- $V_{Cr2+}$ is the volume of Cr2+ solution in liters
- Determine total moles of O2 consumed
From the balanced chemical reaction, we note that 1 mole of Cr2+ reacts with 1/2 mole of O2 to form Cr3+. Hence, the moles of O2 consumed is given by:
$$ n_{O2, consumed} = \frac{1}{2} n_{Cr2+} $$
- Calculate moles of O2 at the start
If $n_{O2, initially}$ is the initial moles of O2 before the reaction, then after the reaction the remaining moles is:
$$ n_{O2, remaining} = n_{O2, initially} - n_{O2, consumed} $$
This gives us the initial moles of O2 before the reaction.
- Use Ideal Gas Law to find initial pressure of O2
To find the initial pressure of O2, we can use the Ideal Gas Law:
$$ PV = nRT $$
Rearranging gives:
$$ P_{initial} = \frac{n_{O2, initially} \cdot R \cdot T}{V_{O2}} $$
Where:
- $R$ is the ideal gas constant (0.0821 L·atm/(K·mol))
- $T$ is temperature in Kelvin
- $V_{O2}$ is the volume of the oxygen gas
We will substitute $n_{O2, initially}$ calculated in the previous steps.
The initial pressure of the oxygen gas can be calculated using:
$$ P_{initial} = \frac{n_{O2, initially} \cdot R \cdot T}{V_{O2}} $$
More Information
The initial pressure calculation assumes ideal gas behavior and relates to stoichiometry in chemical reactions. The relationship between moles, temperature, and pressure through the gas law is what enables us to find this unknown.
Tips
- Forgetting to convert units, especially volume to liters when using concentrations.
- Misapplying the stoichiometry, such as incorrect mole ratios based on the balanced equation.
- Not using the correct gas constant for the units being used.
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