Suppose you had sulfur hexafluoride as your unknown. It has a cost of $200 for 5 pounds of the substance.
If your syringe has a volume of 125.0 mL, the room temperature was 78F, and the pressure was 755
mmHg, what would it cost to fill your syringe 3 times to determine its molecular mass? (Assume there is
no loss of SF6 when filling your syringe.)
dr. BOB is the answer 20 cents?
To determine the cost of filling your syringe with sulfur hexafluoride (SF6) three times, we need to calculate the amount of SF6 needed and then multiply it by the cost.
1. Convert the volume of the syringe from mL to liters:
125.0 mL = 0.125 L
2. Use the ideal gas law to calculate the amount of SF6 needed:
PV = nRT
Where:
P = Pressure = 755 mmHg
V = Volume = 0.125 L
n = moles of SF6
R = Ideal gas constant = 0.0821 L.atm/mol.K
T = Temperature in Kelvin
Convert room temperature from Fahrenheit to Kelvin:
T(K) = (T(F) + 459.67) / 1.8 = (78 + 459.67) / 1.8 = 298.15 K
Now we can calculate the moles of SF6 using the ideal gas law:
755 mmHg * 0.125 L = n * 0.0821 L.atm/mol.K * 298.15 K
Solve for n:
n = (755 mmHg * 0.125 L) / (0.0821 L.atm/mol.K * 298.15 K)
3. Calculate the amount of SF6 needed to fill the syringe three times:
Amount of SF6 = n * Molecular mass of SF6
The molecular mass of SF6 is 32.07 g/mol.
Amount of SF6 needed = n * 32.07 g/mol
= (n * 32.07 g/mol) * 3
4. Calculate the cost of SF6:
Cost = (Amount of SF6 needed / 5 pounds) * $200
Now, you can input the values into the formulas to get the final cost.
To determine the cost of filling your syringe three times with sulfur hexafluoride (SF6), we need to calculate the number of moles of SF6 required and then multiply it by the cost per mole.
First, we need to determine the volume of SF6 required to fill the syringe. Since the syringe has a volume of 125.0 mL (milliliters), we need to convert it to liters by dividing by 1000:
125.0 mL / 1000 = 0.125 L
Next, we can use the Ideal Gas Law equation to calculate the number of moles of SF6. The Ideal Gas Law is given by:
PV = nRT
Where:
P = pressure in atm (atmospheres)
V = volume in L (liters)
n = number of moles
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature in Kelvin (K)
First, we need to convert the temperature from Fahrenheit to Kelvin. The conversion formula is:
TF = TC * (9/5) + 32
Where:
TF = temperature in Fahrenheit
TC = temperature in Celsius
Given that the room temperature is 78°F, we convert it to Celsius:
TC = (78 - 32) * (5/9)
= 46 * (5/9)
= 25.5556 °C
Next, we convert Celsius to Kelvin by adding 273.15:
TK = TC + 273.15
= 25.5556 + 273.15
= 298.7056 K
Now we have all the values to calculate the number of moles:
n = PV / RT
= (755 mmHg * 0.125 L) / (0.0821 L·atm/(mol·K) * 298.7056 K)
= 962.875 mmHg·L / (0.0821 L·atm/(mol·K) * 298.7056 K)
= 962.875 /(0.0821 * 298.7056) mol
= 962.875 / 24.85421856 mol
= 38.79884787 mol
Since we are filling the syringe three times, we need to multiply the number of moles by 3:
n_total = 38.79884787 mol * 3
= 116.3965436 mol
Now, we can calculate the cost by multiplying the number of moles by the cost per mole:
cost = $200 / 5 lb * 1 lb / 453.59237 g * 116.3965436 mol * 146.06 g/mol
= $200 / 5 lb * 1 lb / 453.59237 g * 116.3965436 mol * 146.06 g/mol
≈ $16248.58
Therefore, it would cost approximately $16248.58 to fill your syringe three times to determine the molecular mass of SF6.