If you place 1.26 g of solid silicon in a 6.54 L flask that contains CH3Cl with a pressure of 634 mm Hg at 25°C, what mass of dimethyldichlorosilane, (CH3)2SiCl2(g), can be formed?
Well, what do you call a silicon that ended up in a flask with CH3Cl? A misplaced chip! As for the mass of dimethyldichlorosilane that can be formed, let's calculate it out.
To solve this, we need to use the ideal gas law, PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature. But before we do that, let's convert 634 mm Hg to atm.
634 mm Hg * (1 atm / 760 mm Hg) = 0.83552 atm
Now, let's rearrange the ideal gas law to solve for the number of moles:
n = (PV) / (RT)
P = 0.83552 atm
V = 6.54 L
R = 0.0821 L·atm/mol·K
T = 25°C = 25 + 273.15 K
n = (0.83552 atm * 6.54 L) / (0.0821 L·atm/mol·K * 298.15 K)
n ≈ 0.2215 mol
Now, according to the balanced chemical equation, we have a one-to-one mole ratio between solid silicon and dimethyldichlorosilane. So, the mass of dimethyldichlorosilane can be calculated using the molar mass of (CH3)2SiCl2:
Molar mass of (CH3)2SiCl2 = 129.04 g/mol
Mass of dimethyldichlorosilane = n * molar mass
Mass ≈ 0.2215 mol * 129.04 g/mol
Mass ≈ 28.58 g
Therefore, approximately 28.58 g of dimethyldichlorosilane can be formed. Just remember that I'm a Clown Bot, so take these calculations with a grain of Silly-con.
To answer this question, we need to use the ideal gas law and stoichiometry.
Step 1: Find the number of moles of CH3Cl using the ideal gas law equation:
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)
First, convert the pressure from mm Hg to atm:
634 mm Hg * (1 atm / 760 mm Hg) = 0.8342 atm
Now, convert the temperature from °C to Kelvin:
25°C + 273.15 = 298.15 K
Using the ideal gas law equation, we can rearrange it to solve for the number of moles:
n = PV / RT
= (0.8342 atm) * (6.54 L) / (0.0821 L.atm/mol.K * 298.15 K)
= 0.2127 moles of CH3Cl
Step 2: Write the balanced equation for the reaction:
Si(s) + 2CH3Cl(g) → (CH3)2SiCl2(g)
This equation tells us that one mole of silicon reacts with two moles of CH3Cl to produce one mole of (CH3)2SiCl2.
Step 3: Determine the limiting reagent:
To determine the limiting reagent, we compare the moles of each reactant to their stoichiometric ratio in the equation.
In this case, we have 0.2127 moles of CH3Cl and we need to calculate the number of moles of silicon:
Since the molar mass of Si is 28.0855 g/mol, we can calculate the number of moles:
moles of Si = mass / molar mass
= 1.26 g / 28.0855 g/mol
= 0.0449 moles of Si
Now, compare the moles of each reactant to the stoichiometric ratio:
Si:CH3Cl = 0.0449 moles : 0.2127 moles ≈ 1 : 4.739
Since the ratio is greater than 1, it means the silicon is the limiting reagent.
Step 4: Calculate the mass of (CH3)2SiCl2 that can be formed:
From the balanced equation, we know that 1 mole of silicon reacts with 2 moles of CH3Cl to produce 1 mole of (CH3)2SiCl2.
Therefore, the number of moles of (CH3)2SiCl2 formed is equal to the moles of silicon:
moles of (CH3)2SiCl2 = 0.0449 moles
Finally, we can calculate the mass of (CH3)2SiCl2 using its molar mass:
mass = moles of (CH3)2SiCl2 * molar mass
= 0.0449 moles * (62.5351 g/mol + 2 * 35.453 g/mol)
= 5.15 g
Therefore, the mass of dimethyldichlorosilane, (CH3)2SiCl2, that can be formed is approximately 5.15 g.
To determine the mass of dimethyldichlorosilane that can be formed, we need to use stoichiometry, which involves the balanced chemical equation for the reaction between solid silicon and CH3Cl:
Si(s) + 2 CH3Cl(g) → (CH3)2SiCl2(g)
The coefficients in the balanced equation give us the ratio of moles between the reactants and products.
Step 1: Convert given quantities to moles.
First, let's calculate the moles of CH3Cl present in the flask. To do this, we'll use the ideal gas law equation:
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)
Converting the pressure from mm Hg to atm:
634 mm Hg × (1 atm / 760 mm Hg) = 0.8342 atm
Now we can calculate the number of moles of CH3Cl:
n(CH3Cl) = (P × V) / (R × T)
= (0.8342 atm × 6.54 L) / (0.0821 L·atm/mol·K × 298 K)
≈ 0.2233 mol
Step 2: Determine the limiting reactant.
Next, we need to determine the limiting reactant by comparing the moles of silicon and CH3Cl. The stoichiometric ratio from the balanced equation tells us that 1 mol of silicon reacts with 2 mol of CH3Cl to produce 1 mol of (CH3)2SiCl2.
Given the moles of CH3Cl (0.2233 mol) and the molar ratio, we can calculate the maximum moles of (CH3)2SiCl2 that can be formed:
Max moles of (CH3)2SiCl2 = 0.2233 mol × (1 mol (CH3)2SiCl2 / 2 mol CH3Cl)
≈ 0.1116 mol
Step 3: Convert moles of (CH3)2SiCl2 to mass.
Finally, we can calculate the mass of (CH3)2SiCl2 formed using its molar mass (which can be found in a periodic table):
Molar mass of (CH3)2SiCl2 = (12.01 g/mol × 2) + (1.01 g/mol × 6) + (28.09 g/mol) + (2 × 35.45 g/mol)
= 115.09 g/mol
Mass of (CH3)2SiCl2 = moles × molar mass
= 0.1116 mol × 115.09 g/mol
≈ 12.85 g
Therefore, approximately 12.85 g of dimethyldichlorosilane, (CH3)2SiCl2, can be formed.