The reaction 2 H2O2(aq)->2 H2O(l) + O2(g) is first order in H2O2 and under certain conditions has a rate constant of 0.00752 s-1 at 20.0 C. A reaction vessel initially contains 150.0mL of 30.0% H2O2 by mass solution (the density of the solution is 1.11 g >mL). The gaseous oxygen is collected over water at 20.0 C as it forms. What volume of O2 forms in 85.0 seconds at a barometric pressure of 742.5 mmHg? (The vapor pressure of water at this temperature is 17.5 mmHg.)

Understanding first order reactions is crucial when studying chemical kinetics. These reactions have a rate that is directly proportional to the concentration of one reactant. In practice, this means that as the reactant is consumed during the reaction, the rate decreases. First order reactions follow the integrated rate law:
\( c(t) = c(0) * e^{-kt} \)
where \( c(t) \) is the concentration at time \( t \), \( c(0) \) is the initial concentration, \( k \) is the rate constant, and \( t \) is the elapsed time. The unique feature of first order reactions is that the time taken for the concentration of the reactant to halve, known as the half-life, remains constant, regardless of the initial concentration.

The rate constant, symbolized by \( k \), is the proportionality factor in the rate law equation. It's crucial because it quantifies the speed of a chemical reaction. For first order reactions, the rate constant has the units of \( s^{-1} \) and is specific to the reaction and conditions, such as temperature. By knowing the rate constant and initial conditions, one can calculate how fast a reactant will be consumed or how quickly a product will be formed. When conditions such as temperature change, the rate constant will also change, which reflects on the reaction's speed.

Stoichiometry is essentially the math behind chemistry. It involves using the balanced chemical equation to relate the quantities of reactants and products. In a balanced equation like \( 2 \text{H}_2\text{O}_2 \rightarrow 2 \text{H}_2\text{O} + \text{O}_2 \), the coefficients indicate the ratios in which molecules react and are formed. For instance, two molecules of hydrogen peroxide (\text{H}_2\text{O}_2) produce one molecule of oxygen (\text{O}_2). This ratio is crucial when calculating how much product is made from a known quantity of reactant. Failing to consider stoichiometry in calculations could result in significant errors in the predicted outcome of chemical reactions.

Gas laws are a set of laws that relate the pressure, volume, and temperature of a gas to each other. In chemical reactions producing gases, these laws become particularly important for predicting and measuring the behavior of the gas. The ideal gas law combines several individual laws and is represented by the equation:
\( PV = nRT \), where \( P \) is the pressure, \( V \) is the volume, \( n \) is the number of moles of gas, \( R \) is the ideal gas constant, and \( T \) is the temperature in Kelvin. This law allows us to calculate the volume of a gas produced in a reaction by taking into account the number of moles of gas, the pressure it's under, and the temperature. It is essential to adjust the pressure to account for factors such as water vapor when collecting gas over water, as seen in the provided exercise.