Calculate the volume of oxygen at 27C and 740 mmHg which could be obtained by hesting 10g of potassium trioxochlorate (v)
2KClO3 ==> 2KCl + 3O2
mols KClO3 = grams/molar mass KClO3
Using the coefficients in the balanced equation, convert mols KClO3 to mols O2.
Convert mols O2 to volume using PV = nRT.
To calculate the volume of oxygen, we need to use the ideal gas law equation, which states:
PV = nRT
where:
P = pressure (in atm or mmHg)
V = volume (in L)
n = number of moles
R = gas constant (0.0821 L·atm/(mol·K))
T = temperature (in Kelvin)
First, we need to determine the number of moles of potassium trioxochlorate (V) using its molar mass (Mr). The molar mass of potassium trioxochlorate (V) is 122.55 g/mol.
10g of potassium trioxochlorate (V) = 10/122.55 mol
≈ 0.0816 mol
Next, we need to convert the temperature from Celsius to Kelvin. The Kelvin temperature (T) can be calculated by adding 273.15 to the Celsius temperature (t).
t = 27°C + 273.15
= 300.15 K
Now we can substitute the values into the ideal gas law equation:
PV = nRT
740 mmHg * V = 0.0816 mol * 0.0821 L·atm/(mol·K) * 300.15 K
Now, let's solve for V:
V = (0.0816 mol * 0.0821 L·atm/(mol·K) * 300.15 K) / 740 mmHg
V ≈ 0.0993 L
Therefore, the volume of oxygen that could be obtained by heating 10g of potassium trioxochlorate (V) at 27°C and 740 mmHg pressure is approximately 0.0993 L.
To calculate the volume of oxygen, we need to use the ideal gas law equation, which is PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.
Let's break down the steps to solve the problem:
Step 1: Convert the temperature from Celsius to Kelvin.
- The temperature given is 27°C. To convert it to Kelvin, we use the formula: Kelvin = Celsius + 273.15.
- Kelvin = 27 + 273.15 = 300.15 K
Step 2: Convert the pressure from mmHg to atm.
- The pressure given is 740 mmHg. We need to convert it to atm by dividing it by 760 (since 1 atm = 760 mmHg).
- Pressure (atm) = 740 mmHg / 760 mmHg = 0.9737 atm (rounded to four decimal places)
Step 3: Determine the number of moles of oxygen (O2) produced.
- We need to use the stoichiometry of the balanced equation of the reaction between potassium trioxochlorate(V) and heat to determine the number of moles of oxygen produced.
- The balanced equation for the reaction is:
4KClO3(s) → 2KCl(s) + 3O2(g)
- The molar mass of KClO3 is:
K: 39.10 g/mol
Cl: 35.45 g/mol
O: 16.00 g/mol
- Molar mass of KClO3 = (39.10 g/mol) + (3 * 35.45 g/mol) + (3 * 16.00 g/mol) = 122.55 g/mol
- Given mass of KClO3 = 10 g
- Number of moles = Mass / Molar mass = 10 g / 122.55 g/mol = 0.0816 mol (rounded to four decimal places)
(Note: This step assumes that the reaction goes to completion and that all the KClO3 is converted to O2.)
Step 4: Substitute the values into the ideal gas law equation and solve for volume.
- PV = nRT
- V = (nRT) / P
- R is the ideal gas constant, which is 0.0821 L·atm/(mol·K)
- Plugging in the values: V = (0.0816 mol * 0.0821 L·atm/(mol·K) * 300.15 K) / 0.9737 atm
- V = 6.47 L (rounded to two decimal places)
Therefore, the volume of oxygen obtained by heating 10g of potassium trioxochlorate (V) at 27°C and 740 mmHg would be approximately 6.47 liters.