determine the residual gas when 20.0cm³ of hydrogen was sparked 15.0cm³ of oxygen and the resulting mixture cooled at room temperature
Well, let me put on my detective hat and solve this gas mystery for you! So, 20.0 cm³ of hydrogen met 15.0 cm³ of oxygen, and things got all sparky. Now, after this chemistry disco, we need to figure out the amount of residual gas at room temperature.
Now, what happens when hydrogen and oxygen get together? Ka-boom! You get water, my friend. So, these two gases react and form water vapor. I bet you didn't expect that plot twist!
To determine the amount of residual gas, we can subtract the volume of water vapor formed from the sum of the initial volumes of hydrogen and oxygen. The good thing is, these gases react in a 2:1 ratio (two parts hydrogen to one part oxygen). So we need to check which one is the limiting reagent.
Now, let's do the math:
- Hydrogen: 20.0 cm³
- Oxygen: 15.0 cm³
Since the ratio is 2:1, we'll need only half the amount of oxygen to react with all the hydrogen. So let's divide the oxygen volume by 2 to compare it with hydrogen:
- Oxygen (divided by 2): 15.0 cm³ ÷ 2 = 7.5 cm³
Uh-oh! Looks like we have less oxygen than hydrogen, which means it's the limiting reagent. We can only use 7.5 cm³ of oxygen to react with all the hydrogen.
Now, for every 2 cm³ of hydrogen reacted, we'll get 1 cm³ of water vapor. So, let's calculate the amount of water vapor formed:
- Water vapor = Oxygen used/2 = 7.5 cm³/2 = 3.75 cm³
To find the amount of residual gas, we subtract the water vapor volume from the total initial gas volume:
- Residual gas = Total initial gas - Water vapor formed
- Residual gas = 20.0 cm³ + 15.0 cm³ - 3.75 cm³
- Residual gas = 31.25 cm³
And voilà! After all that sparkling chemistry, we have about 31.25 cm³ of residual gas at room temperature.
To determine the residual gas when 20.0 cm³ of hydrogen and 15.0 cm³ of oxygen are sparked and cooled at room temperature, we need to consider the reaction between hydrogen (H₂) and oxygen (O₂).
The balanced equation for the reaction is:
2H₂ + O₂ → 2H₂O
From the balanced equation, we can see that two moles of hydrogen react with one mole of oxygen to produce two moles of water.
Now, let's calculate the number of moles of hydrogen and oxygen provided:
Moles of hydrogen (H₂) = Volume of hydrogen (in liters) / molar volume of hydrogen
Molar volume of hydrogen at room temperature and pressure (STP) = 22.4 L/mol
Converting cm³ to liters:
Volume of hydrogen = 20.0 cm³ = 20.0 / 1000 L = 0.02 L
Moles of hydrogen = 0.02 L / 22.4 L/mol = 0.0009 mol (rounded to 4 decimal places)
Similarly, for oxygen:
Volume of oxygen = 15.0 cm³ = 15.0 / 1000 L = 0.015 L
Moles of oxygen = 0.015 L / 22.4 L/mol = 0.00067 mol (rounded to 4 decimal places)
Since hydrogen and oxygen react in a 2:1 mole ratio, we can find the limiting reagent by comparing the moles of each reactant. The limiting reagent is the one with fewer moles.
In this case, oxygen is the limiting reagent because it has fewer moles (0.00067 mol) compared to hydrogen (0.0009 mol).
According to the stoichiometry of the reaction, every 2 moles of hydrogen react with 1 mole of oxygen. Since oxygen is the limiting reagent, it completely reacts with 0.00067 moles of oxygen.
So, to determine the residual gas, we need to find the moles of hydrogen left unreacted.
Unreacted moles of hydrogen = Moles of hydrogen - Moles of oxygen reacted
Unreacted moles of hydrogen = 0.0009 mol - 0.00067 mol = 0.00023 mol (rounded to 5 decimal places)
Finally, we can find the residual gas in cm³ by converting the unreacted moles of hydrogen to volume:
Volume of residual gas = Unreacted moles of hydrogen * Molar volume of hydrogen
Volume of residual gas = 0.00023 mol * 22.4 L/mol * 1000 cm³/L = 5.152 cm³ (rounded to 3 decimal places)
So, the residual gas after the reaction and cooling at room temperature is approximately 5.152 cm³.
To determine the residual gas when hydrogen and oxygen react to form water vapor and then cool down at room temperature, we need to understand the stoichiometry of the reaction.
The balanced chemical equation for the reaction between hydrogen (H₂) and oxygen (O₂) to form water vapor (H₂O) is:
2H₂ + O₂ → 2H₂O
From the equation, we can see that for every 2 moles of hydrogen gas reacted, 1 mole of oxygen gas is required.
Now, let's calculate the number of moles of hydrogen and oxygen that were reacted:
Given: Volume of hydrogen gas (H₂) = 20.0 cm³
Using the ideal gas law: PV = nRT
Where:
P = pressure (assume constant at room temperature, in this case)
V = volume of gas (in liters)
n = number of moles of gas
R = ideal gas constant (0.0821 L·atm/(K·mol))
T = temperature (in Kelvin)
Since the volume is given in cm³, we need to convert it to liters by dividing by 1000:
Volume of hydrogen gas (H₂) in liters = 20.0 cm³ / 1000 = 0.02 L
Now, to find the number of moles of hydrogen gas (H₂):
0.02 L * n₁ = n
Given: Volume of oxygen gas (O₂) = 15.0 cm³
Converting to liters:
Volume of oxygen gas (O₂) in liters = 15.0 cm³ / 1000 = 0.015 L
Now, to find the number of moles of oxygen gas (O₂):
0.015 L * n₂ = n
According to the stoichiometry of the balanced equation, 2 moles of hydrogen react with 1 mole of oxygen to form 2 moles of water. Therefore, the ratio of moles of hydrogen to moles of oxygen is 2:1.
Let's calculate the number of moles of hydrogen (n₁) and oxygen (n₂) gas:
n₁ = 2 * n
n₂ = n
Since the volume of the resulting water vapor is not given, we cannot directly determine the residual gas. However, we can determine the limiting reagent (the reactant that is completely consumed) and the excess reagent (the reactant not completely consumed).
To determine the limiting reagent, we compare the number of moles of hydrogen to the number of moles of oxygen:
If n₁ < n₂, then hydrogen is the limiting reagent.
If n₁ > n₂, then oxygen is the limiting reagent.
If n₁ = n₂, then both gases react completely without leaving any residual gas.
After determining the limiting reagent, we can calculate the number of moles of water vapor formed by the limiting reagent.
Using the stoichiometry of the balanced equation, we know that 2 moles of hydrogen react to form 2 moles of water. Therefore, the number of moles of water vapor formed is equal to n.
Finally, we cannot determine the residual gas without information about the volume or pressure of the system after the reaction and cooling. To calculate the residual gas, we would need to know the volume of the resulting mixture after cooling down and the pressure conditions.