Reaction Rate = -(1/2) [d(H2O2)/dt] = [d(O2)/ dt]
Using 25 mL of a 0.2 M hydrogen peroxide solution, the following results are obtained from the equation above: 8.62 mL of gas is collected in 120 seconds. (Assume 760 Torr = 1 atm) Room temperature is 25 degrees C and the vapor pressure of water is 24 Torr.
a) How many moles of oxygen are produced per second?
b) What is the rate of the reaction [d(O2)/dt]?
c) What is the change in the concentration of H2O2 per second?
To answer these questions, we need to use the given information and the equation for the reaction rate. Let's break down the problem step by step:
a) How many moles of oxygen are produced per second?
To find the number of moles of oxygen produced per second, we first need to calculate the volume of oxygen produced per second.
Given:
Volume of oxygen collected = 8.62 mL = 0.00862 L (convert from milliliters to liters)
Time = 120 seconds
To calculate the volume of oxygen produced per second, we divide the total volume of oxygen collected by the time taken:
Volume of oxygen per second = (0.00862 L) / (120 s) = 7.18 x 10^-5 L/s
Now, we can use the ideal gas law to calculate the number of moles of oxygen produced:
PV = nRT
Where:
P = pressure (in atm)
V = volume (in liters)
n = number of moles
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature (in Kelvin)
We need to account for the vapor pressure of water, so the pressure inside the container is the total pressure minus the vapor pressure of water.
Total pressure = 760 Torr = 1 atm
Vapor pressure of water = 24 Torr
Pressure of oxygen = Total pressure - Vapor pressure of water = (760 - 24) Torr = 736 Torr = 0.967 atm
Now we can rearrange the ideal gas law equation to solve for n:
n = PV / RT
n = (0.967 atm) x (0.00862 L) / [(0.0821 L·atm/(mol·K)) x (298 K)] = 0.000308 moles
Therefore, the number of moles of oxygen produced per second is 0.000308 moles.
b) What is the rate of the reaction [d(O2)/dt]?
From the given reaction rate equation, we know that the rate of the reaction is equal to the negative of the rate of change of hydrogen peroxide, which is equal to the rate of change of oxygen.
Therefore, the rate of the reaction [d(O2)/dt] is given by:
[d(O2)/dt] = 0.000308 moles/s
c) What is the change in the concentration of H2O2 per second?
To calculate the change in the concentration of H2O2 per second, we need to know the stoichiometry of the reaction. From the balanced equation, we know that the ratio of the rate of change of hydrogen peroxide to the rate of change of oxygen is 1:1.
Therefore, the change in the concentration of H2O2 per second is also given by:
[d(H2O2)/dt] = [d(O2)/dt] = 0.000308 moles/s
So, the change in the concentration of H2O2 per second is 0.000308 moles/s.