what is molar concentration of a solution obtained by dissolving 560cm of hydrogen chloride gas at s.t.p in 92.5cm of water
Technically I don't know because we need the volume of the solution. I assume the problem maker wants that 92.5 cc (you meant cm^3 I'm sure) to be the volume of the solution. One mole of a gas at STP will occupy 22.4L; therefore, moles HCl gas = 550 cc/22,400 cc.
Then moles HCl/L soln = M
To calculate the molar concentration of a solution, we need to know the volume of the solvent (in this case, water) and the moles of solute (in this case, hydrogen chloride gas).
Step 1: Convert the given volumes to liters.
560 cm³ = 560/1000 = 0.56 L (conversion from cm³ to L)
92.5 cm³ = 92.5/1000 = 0.0925 L
Step 2: Calculate the number of moles of hydrogen chloride gas.
To determine the number of moles, we can use the ideal gas law, which states that PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.
At standard temperature and pressure (STP):
- Pressure (P) = 1 atm
- Volume (V) = 0.56 L (Volume of hydrogen chloride gas)
The ideal gas constant (R) is 0.0821 L.atm/(mol.K), and T = 273.15 K.
Using the ideal gas law, we can rearrange the equation to solve for n (number of moles):
n = PV / RT
n = (1 atm)(0.56 L) / (0.0821 L.atm/(mol.K) * 273.15 K)
n = 0.022 moles
Step 3: Calculate the molar concentration.
Molar concentration is defined as moles of solute divided by the volume of the solution in liters.
Molar Concentration (M) = moles / volume
Molar Concentration = 0.022 moles / 0.0925 L
Molar Concentration = 0.238 M (rounded to three decimal places)
Therefore, the molar concentration of the hydrogen chloride gas solution is 0.238 M.
To find the molar concentration of a solution, we need to first calculate the number of moles of the solute (hydrogen chloride gas in this case) and then divide it by the volume of the solution.
Here's how you can calculate it step by step:
1. Convert the volume of the hydrogen chloride gas from cm³ to liters:
560 cm³ ÷ 1000 = 0.56 L (since 1 L = 1000 cm³)
2. Convert the volume of water from cm³ to liters:
92.5 cm³ ÷ 1000 = 0.0925 L
3. Calculate the number of moles of hydrogen chloride gas (HCl) using the ideal gas law:
PV = nRT
Given:
P = pressure at standard temperature and pressure (s.t.p.) = 1 atm
V = volume of gas in liters = 0.56 L
R = ideal gas constant = 0.0821 L·atm/(mol·K)
T = temperature at s.t.p. = 273 K
n = (PV) / (RT)
= (1 atm * 0.56 L) / (0.0821 L·atm/(mol·K) * 273 K)
≈ 0.0252 moles (rounded to 4 decimal places)
4. Calculate the molar concentration of the solution by dividing the number of moles of HCl by the total volume of the solution:
Molar concentration = Moles of solute (HCl) / Volume of solution
Volume of solution = volume of HCl gas + volume of water
= 0.56 L + 0.0925 L
≈ 0.6525 L (rounded to 4 decimal places)
Molar concentration = 0.0252 moles / 0.6525 L
≈ 0.0386 M (rounded to 4 decimal places)
Therefore, the molar concentration of the solution obtained by dissolving 560 cm³ of hydrogen chloride gas at s.t.p. in 92.5 cm³ of water is approximately 0.0386 M.