If the methane contained in 3.50L of a saturated solution at 25 ∘C was extracted and placed under STP conditions, what volume would it occupy?
Solubility of methane is 1.3 millimolar
M = mols/L
0.0013 M = mols/3.50L
mols = 0.0013 mols/L x 3.50L = estimated 0.005 mols but you need to do that more accurately.
Then substitute for n in PV = nRT with other conditions and solve for volume.
Well, if we're talking about extracting the methane from a saturated solution, I hope you brought your methane extraction kit! Let's calculate the volume it would occupy.
First, we need to convert the solubility of methane from millimolar to moles per liter. Given that the solubility is 1.3 millimolar, we can multiply it by 1 mole/1000 millimoles to get the solubility as 0.0013 moles per liter.
Now that we know the number of moles of methane in the 3.50L of solution, we can use the ideal gas law to calculate the volume under STP conditions.
According to the ideal gas law, 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.
Since we're assuming standard temperature and pressure (STP), we can use the values of P = 1 atm and T = 273 K.
Rearranging the equation, we get V = nRT/P.
Plugging in the values, we have V = (0.0013 mol/L)(0.0821 L·atm/mol·K)(273 K)/(1 atm).
After crunching the numbers, the volume would be approximately... *drumroll*... 0.0309 L or 30.9 milliliters. That's a lot smaller than the initial 3.50L, so I hope you brought a shrink ray with you too!
To solve this problem, we need to convert the given volume of the solution into moles, and then use the ideal gas law to determine the volume of methane at STP.
1. Convert the volume of the solution to liters of methane:
Since the solubility of methane is given in millimolar (mM), we need to convert the solubility to moles per liter (M).
1.3 mM of methane = 1.3 × 10^(-3) moles of methane per liter (M)
2. Calculate the number of moles of methane in the solution:
moles of methane = solubility (M) × volume of solution (liters)
moles of methane = (1.3 × 10^(-3) mol/L) × (3.50 L)
moles of methane = 4.55 × 10^(-3) moles
3. Use the ideal gas law to determine the volume of methane at STP:
The ideal gas law is given as PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant (0.0821 L·atm/(mol·K)), and T is the temperature in Kelvin (K).
Since the volume of methane at STP is unknown, we can represent it as V.
The STP conditions are typically defined as a temperature of 0 °C (273.15 K) and a pressure of 1 atm.
Setting up the equation:
PV = nRT
(1 atm) × V = (4.55 × 10^(-3) mol) × (0.0821 L·atm/(mol·K)) × (273.15 K)
4. Solve for V, the volume of methane at STP:
V = (4.55 × 10^(-3) mol) × (0.0821 L·atm/(mol·K)) × (273.15 K)
V ≈ 0.98 liters (rounded to two decimal places)
Therefore, the volume of methane extracted from the solution at STP conditions would occupy approximately 0.98 liters.
To solve this problem, we need to convert the given volume of the saturated solution to moles of methane. Then, we can use the ideal gas law to determine the volume of methane at STP conditions.
Step 1: Convert the volume of the saturated solution to moles of methane.
We know that the solubility of methane is given as 1.3 millimolar. A millimolar is a unit of concentration, and it represents the number of moles of solute (in this case, methane) per liter of solution. Therefore, we can assume that the concentration of methane in the saturated solution is 1.3 millimoles per liter.
To convert the volume of the saturated solution to moles of methane, we can multiply the concentration (in moles per liter) by the volume of the solution in liters:
Number of moles of methane = Concentration of methane (in moles per liter) x Volume of solution (in liters)
Number of moles of methane = 1.3 x 10^(-3) moles/L x 3.50 L
Step 2: Calculate the volume of methane at STP.
Under STP conditions (Standard Temperature and Pressure), the volume occupied by one mole of any gas is 22.4 liters. Therefore, we can use the ideal gas law to calculate the volume of methane at STP:
PV = nRT
Where:
P = Pressure (under STP, P = 1 atm)
V = Volume of gas at STP (what we need to find)
n = Number of moles of gas
R = Ideal gas constant (0.0821 L·atm/mol·K)
T = Temperature (under STP, T = 273 K)
Simplifying the equation, we get:
V = (nRT) / P
Here, n is the number of moles we calculated in Step 1, R is the ideal gas constant, P is 1 atm, and T is 273 K.
Now, we can substitute these values to calculate the volume of methane at STP:
V = (3.50 L) x (1.3 x 10^(-3) moles/L) x (0.0821 L·atm/mol·K) x (273 K) / 1 atm
After performing the calculations, the volume of methane at STP can be determined.