A sample of gas contains 0.1900 mol of HBr(g) and 9.500×10-2 mol of Cl2(g) and occupies a volume of 11.2 L. The following reaction takes place:
2HBr(g) + Cl2(g)2HCl(g) + Br2(g)
Calculate the volume of the sample after the reaction takes place, assuming that the temperature and the pressure remain constant.
Looks unchanged to me.
3 moles -> 3 moles
well, maybe not. There will be no volume change if everything reacts, If there are fractional parts left over, they will make their own contributions. So, yeah, find how many moles reacted, and so forth.
To determine the volume of the gas after the reaction takes place, we need to use the mole ratio from the balanced chemical equation and the ideal gas law.
First, let's calculate the number of moles of HCl and Br2 produced by the reaction.
From the balanced chemical equation, we can see that the mole ratio of HBr to HCl is 2:2, and the mole ratio of HBr to Br2 is 2:1.
Since we have 0.1900 mol of HBr, we will produce the same number of moles of HCl. Therefore, we have 0.1900 mol of HCl.
Using the same reasoning, we have 0.1900 mol of HBr, which means we will produce 0.1900/2 = 0.0950 mol of Br2.
Now, let's use the ideal gas law to calculate the volume. The ideal gas law is given by:
PV = nRT
Where:
P is the pressure, which remains constant
V is the volume, what we want to calculate
n is the number of moles of gas
R is the ideal gas constant (0.0821 L·atm/mol·K)
T is the temperature, which remains constant
Since the pressure and temperature remain constant throughout the reaction, we can rewrite the ideal gas law as:
V1/n1 = V2/n2
Where:
V1 is the initial volume of the sample
n1 is the initial total number of moles of gas
V2 is the volume after the reaction
n2 is the total number of moles of gas after the reaction
Plugging in the values into the equation:
V1/ (0.1900 + 0.0950) = V2 / (0.1900 + 0.1900 + 0.0950 + 0.0950)
V1 / 0.2850 = V2 / 0.5700
Cross-multiplying, we get:
V1 * 0.5700 = V2 * 0.2850
Dividing both sides of the equation by 0.5700, we get:
V2 = V1 * (0.2850 / 0.5700)
V2 = V1 * 0.5
Now, we can substitute the initial volume into the equation:
V2 = 11.2 L * 0.5
V2 = 5.6 L
Therefore, the volume of the sample after the reaction takes place is 5.6 L.
To calculate the volume of the sample after the reaction takes place, we can use the concept of the ideal gas law. The ideal gas law states that the product of the pressure, volume, and number of moles of gas is directly proportional to the temperature of the gas.
The equation for the ideal gas law is: PV = nRT
Where:
P is the pressure of the gas
V is the volume of the gas
n is the number of moles of gas
R is the ideal gas constant (0.0821 L·atm/mol·K)
T is the temperature in Kelvin
In this case, the temperature and pressure are stated to remain constant, so we can treat them as constant values.
Let's begin by calculating the initial volume of the sample before the reaction takes place.
For HBr:
Number of moles of HBr = 0.1900 mol
For Cl2:
Number of moles of Cl2 = 9.500×10-2 mol
The total number of moles of gas before the reaction:
Total moles = moles of HBr + moles of Cl2
Total moles = 0.1900 mol + 9.500×10-2 mol
Total moles = 0.1900 mol + 0.0950 mol
Total moles = 0.2850 mol
Now, we can calculate the initial volume using the ideal gas law:
PV = nRT
P(initial) * V(initial) = n * R * T
Since the pressure and temperature are constant, we can simplify the equation:
V(initial) = (n * R * T) / P(initial)
Substituting the known values:
V(initial) = (0.2850 mol * 0.0821 L·atm/mol·K * T) / P(initial)
Now, let's calculate the volume of the sample after the reaction takes place.
According to the balanced chemical equation, the moles of HBr and Cl2 will react to form HCl and Br2 in a 2:1 ratio.
So, the number of moles of HBr that will react is:
moles of HBr reacted = (0.1900 mol) / 2
moles of HBr reacted = 0.0950 mol
Therefore, the moles of Cl2 that react is half of that:
moles of Cl2 reacted = 0.0950 mol / 2
moles of Cl2 reacted = 0.0475 mol
The total moles of gas after the reaction:
Total moles = Total moles before reaction - moles reacted
Total moles = 0.2850 mol - (0.0950 mol + 0.0475 mol)
Total moles = 0.2850 mol - 0.1425 mol
Total moles = 0.1425 mol
Now, we can calculate the final volume using the ideal gas law:
V(final) = (n * R * T) / P(initial)
V(final) = (0.1425 mol * 0.0821 L·atm/mol·K * T) / P(initial)
Remember that for this problem, the temperature and pressure remain constant, so we can cancel them out from the equation. Therefore, the final volume is:
V(final) = (0.1425 mol * 0.0821 L·atm/mol·K) / P(initial)
Now, we need the initial volume, which was given in the question as 11.2 L. We can substitute this value into the equation:
V(final) = (0.1425 mol * 0.0821 L·atm/mol·K) / P(initial)
V(final) = (0.1425 mol * 0.0821 L·atm/mol·K) / 11.2 L
V(final) ≈ 0.001047 L·atm/mol·K
Therefore, the final volume of the sample after the reaction takes place, assuming constant temperature and pressure, is approximately 0.001047 liters.