50cm³ of methane CH4 was exploded with 170cm³ of oxygen gas and underwent complete combustion
CH4+CO2~CO2+2H2O
Determine the total volume of the resultant gaseous mixture and the volume of each gas
The balanced equation for the combustion of methane (CH4) is:
CH4 + 2O2 → CO2 + 2H2O
From the balanced equation, we can see that 1 mole of CH4 reacts with 2 moles of O2 to produce 1 mole of CO2 and 2 moles of H2O.
To find the volume ratio, we need to consider the mole ratio. Since the volume depends on the number of moles, we can use the ratio of the coefficients in the balanced equation to determine the volume ratio.
The coefficients are: CH4 (1), O2 (2), CO2 (1), and H2O (2).
Given that we started with 50 cm³ of CH4 and 170 cm³ of O2, we need to convert the given volumes to moles.
To convert the volumes to moles, we use the ideal gas law equation:
PV = nRT
P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin.
Assuming the temperature and pressure are constant, we can use the following ratio:
(V1 / n1) = (V2 / n2)
Let's denote the volume of methane as V1, the volume of oxygen as V2, the volume of CO2 as V3, and the volume of H2O as V4.
Using the ratio:
V1 / n1 = V2 / n2
50 cm³ / n1 = 170 cm³ / n2
To solve for n1:
n1 = (50 cm³ x n2) / 170 cm³
Similarly, using the ratio:
V3 / n3 = V4 / n4
Let's assume the total volume of the resultant gaseous mixture is V.
Then we can write:
V = V1 + V2 + V3 + V4
The volume ratio is given by:
V1 : V2 : V3 : V4
To find the total volume of the resultant gaseous mixture, we need to solve for V.
V = V1 + V2 + V3 + V4
Since we are given V1 and V2, we can substitute the values and solve for V.
V = 50 cm³ of CH4 + 170 cm³ of O2 + V3 + V4
Now we need to determine the volumes of CO2 and H2O produced.
From the balanced equation, we know that 1 mole of CH4 reacts with 1 mole of CO2 and 2 moles of H2O are produced.
Using the ratio:
n1 : n2 : n3 : n4
1 : 2 : 1 : 2
We have:
n1 = (50 cm³ x n2) / 170 cm³
n3 = n1
n4 = 2n1
Since n1 represents the number of moles of CH4, we can solve for n1 by converting the volume of CH4 (50 cm³) to moles.
To convert the volume to moles, we use the ideal gas law equation:
PV = nRT
Rearranging the equation to solve for n1:
n1 = (PV) / (RT)
Substituting the values:
n1 = (50 cm³ x P) / (RT)
n1 = (50 cm³ x P) / (0.08206 L x atm / mol x K x T)
The temperature and pressure values are not given, so we cannot calculate the exact number of moles of CH4.
However, once we have the value for n1, we can use it to find the values for n2, n3, and n4:
n2 = 2n1
n3 = n1
n4 = 2n1
Now, we can solve for the total volume of the resultant gaseous mixture (V) and the volume of each gas (V1, V2, V3, V4).
However, without the values for n1, n2, n3, n4, P, and T, we cannot determine the exact volumes. You will need to provide those values in order to find the volumes.