At 791 K and relatively low pressures, the gas-phase decomposition of acetaldehyde (CH3CHO) is second order in acetaldehyde. CH3CHO(g) → CH4(g) + CO(g) The total pressure of a particular reaction mixture was found to vary as follows: (a) Use the pressure data to determine the value of the rate constant in units of atm⁻¹ s⁻¹. (b) What is the rate constant in the usual units of M⁻¹ s⁻¹?

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Step 1: Recognize that the decomposition of acetaldehyde is a second-order reaction. For a second-order reaction, the rate law is given by \( \text{Rate} = k [\text{CH}_3\text{CHO}]^2 \), where \( k \) is the rate constant.

Step 2: Use the integrated rate law for a second-order reaction, which is \( \frac{1}{[A]_t} = \frac{1}{[A]_0} + kt \), where \([A]_t\) is the concentration at time \( t \), \([A]_0\) is the initial concentration, and \( k \) is the rate constant.

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Step 3: Convert the pressure data to concentration data. Since the reaction occurs in the gas phase, you can use the ideal gas law \( PV = nRT \) to relate pressure to concentration. Assume constant temperature and volume to simplify calculations.

Step 4: Plot \( \frac{1}{[A]} \) versus time using the converted concentration data. The slope of this line will be equal to the rate constant \( k \) in units of atm⁻¹ s⁻¹.

Step 5: Convert the rate constant from atm⁻¹ s⁻¹ to M⁻¹ s⁻¹. Use the ideal gas law to find the conversion factor between atm and molarity (M), considering the temperature and volume conditions.

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A 0.500 L reaction vessel equipped with a movable piston is filled completely with a 3.00% aqueous solution of hydrogen peroxide. The H2O2 decomposes to water and O2 gas in a first-order reaction that has a half-life of 10.7 h. As the reaction proceeds, the gas formed pushes the piston against a constant external atmospheric pressure of 738 mm Hg. Calculate the PV work done (in joules) after a reaction time of 4.02 h. (You may assume that the density of the solution is 1.00 g/mL and that the temperature of the system is maintained at 20 °C.)

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You may have been told not to mix bleach and ammonia. The reason is that bleach (sodium hypochlorite) reacts with ammonia to produce toxic chloramines, such as NH2Cl. For example, in basic solution: OCl-1aq2 + NH31aq2S OH-1aq2 + NH2Cl1aq2 (a) The following initial rate data for this reaction were obtained in basic solution at 25 °C

What is the rate law for the reaction? What is the numerical value of the rate constant k, including the correct units?

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Verified step by step guidance

1. Step 1: Recognize that the decomposition of acetaldehyde is a second-order reaction. For a second-order reaction, the rate law is given by \( \text{Rate} = k [\text{CH}_3\text{CHO}]^2 \), where \( k \) is the rate constant.
2. Step 2: Use the integrated rate law for a second-order reaction, which is \( \frac{1}{[A]_t} = \frac{1}{[A]_0} + kt \), where \([A]_t\) is the concentration at time \( t \), \([A]_0\) is the initial concentration, and \( k \) is the rate constant.
3. Step 3: Convert the pressure data to concentration data. Since the reaction occurs in the gas phase, you can use the ideal gas law \( PV = nRT \) to relate pressure to concentration. Assume constant temperature and volume to simplify calculations.
4. Step 4: Plot \( \frac{1}{[A]} \) versus time using the converted concentration data. The slope of this line will be equal to the rate constant \( k \) in units of atm⁻¹ s⁻¹.
5. Step 5: Convert the rate constant from atm⁻¹ s⁻¹ to M⁻¹ s⁻¹. Use the ideal gas law to find the conversion factor between atm and molarity (M), considering the temperature and volume conditions.