a)consider the following reaction: Mg(s)+ 2HCl(aq) --> MgCl2 (aq)+H2 (g)
What minimum amount of 1.75 M HCl is necessary to produce 27.5 L of H2 at STP?
b) What is the freezing point of an aqueous solution that boils at 102.1 C?
See above for a.
b).
delta T = Kb*molality.
solve for molality.
delta T = Kf*molality.
solve for delta T. Subtract from 0o to find freezing point.
a) To determine the minimum amount of 1.75 M HCl required to produce 27.5 L of H2 at STP, we need to use the stoichiometry of the given reaction.
From the balanced equation: Mg(s) + 2HCl(aq) -> MgCl2(aq) + H2(g), we can see that the molar ratio between HCl and H2 is 2:1.
1. Convert the volume of H2 to moles:
Using 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:
At STP, the pressure (P) is 1 atm, the temperature (T) is 273.15 K, and the volume (V) is 27.5 L.
Using the equation, we can solve for n:
n = PV / RT
= (1 atm) * (27.5 L) / (0.0821 L·atm/(mol·K) * 273.15 K)
= 1.07 moles of H2
2. Determine the amount of HCl required:
Since the molar ratio between HCl and H2 is 2:1, we need half the amount of HCl in moles. Thus:
Amount of HCl = (1.07 moles of H2) / 2
= 0.54 moles
3. Calculate the volume of 1.75 M HCl required:
The concentration of HCl is given as 1.75 M, which means there are 1.75 moles of HCl per liter of solution. Therefore:
Volume of HCl = 0.54 moles / 1.75 moles/L
= 0.31 L
Therefore, the minimum amount of 1.75 M HCl required to produce 27.5 L of H2 at STP is 0.31 L.
b) The freezing point of an aqueous solution can be determined using the equation:
ΔTF = (Kf)(m)
Where ΔTF is the change in freezing point, Kf is the cryoscopic constant, and m is the molality of the solution.
1. Convert the boiling point of the solution to its freezing point change:
Since boiling point elevation and freezing point depression are opposite effects, ΔTF is the negative of the boiling point elevation, which is 102.1°C - 100.0°C = 2.1°C.
2. Determine the molality of the solution:
The molality of a solution is the moles of solute per kilogram of solvent. Since the question does not provide the solute or solvent, we cannot directly calculate the molality. Additional information is required (e.g., mass or molarity of the solute, mass or density of the solvent).
Please provide more details to determine the freezing point of the aqueous solution.
a) To determine the minimum amount of 1.75 M HCl required to produce 27.5 L of H2 gas at STP (standard temperature and pressure), we need to use stoichiometry and the molar ratio between HCl and H2.
First, let's understand the information given in the question:
- The balanced chemical equation for the reaction is: Mg(s) + 2HCl(aq) → MgCl2(aq) + H2(g).
- From the equation, we can see that for every 2 moles of HCl reacted, 1 mole of H2 is produced. This gives us the molar ratio of H2 to HCl as 1:2.
Now, let's calculate the amount of HCl needed:
1. Determine the moles of H2 required using the ideal gas law at STP:
- According to the ideal gas law, PV = nRT, where:
- P is the pressure of the gas (which is 1 atm at STP),
- V is the volume of the gas (which is 27.5 L),
- n is the number of moles of gas, and
- R is the ideal gas constant (0.0821 L·atm/(mol·K)).
- Rearranging the equation, we have n = PV/RT.
- Substituting the values, we get n = (1 atm) × (27.5 L) / (0.0821 L·atm/(mol·K) × 273 K).
- Calculate the value of n, which represents the number of moles of H2 needed.
2. Since the molar ratio of H2 to HCl is 1:2, we need twice the number of moles of HCl compared to H2.
- Calculate 2 times the value of n obtained in the previous step.
3. Calculate the volume of 1.75 M HCl required, using the molarity formula:
- Molarity (M) = moles of solute / liters of solution.
- Rearranging the equation, we have liters of solution = moles of solute / molarity.
- Substituting the values, we get liters of solution = (2 × n) / 1.75.
- Calculate the value of liters of solution, which represents the minimum amount of 1.75 M HCl required.
b) To determine the freezing point of an aqueous solution that boils at 102.1 °C, we need to use the Colligative Properties of solutions, specifically the freezing point depression.
Freezing point depression is given by the formula:
ΔTf = Kf * m,
where ΔTf is the freezing point depression, Kf is the cryoscopic constant of the solvent, and m is the molality of the solute.
1. Determine the freezing point depression by finding the difference between the freezing point of the pure solvent (in this case, water) and the given boiling point of the solution.
- ΔTf = freezing point of pure solvent - boiling point of the solution.
2. Calculate the molality (m) of the solute using the equation:
- molality (m) = moles of solute / mass of solvent (in kg).
- Rearrange the equation to get moles of solute = m * mass of solvent.
3. In order to calculate the molality, you need to know the mass of the solvent and the moles of the solute. Since these values are not provided in the question, you would need additional information to proceed with the calculation.
Remember, equations and constants mentioned in the explanation above are general and may vary depending on the specific question.