Care must be taken when diluting sulfuric acid with water, because the dilution process is highly exothermic:
H2SO4(l) "arrow" H2SO4(aq) + heat
a) Find the ÄHo for diluting 1.00 mol of H2SO4(l) (d = 1.83 g/mL) to 1 L of 1.00 M H2SO4(aq) (d = 1.060 g/mL).
Suppose you carry out the dilution in a calorimeter. The initial T is 28.8C, and the specific heat capacity of the final solution is 3.50 J/g·K. What is the final T?
is this part correct: -93.52?
what is temperature? Is it 53? thank you
I don't have any of those numbers and if I don't use the same numbers you have the answers will no agree.
To find the ÄHo for diluting 1.00 mol of H2SO4(l) to 1 L of 1.00 M H2SO4(aq), we need to calculate the change in enthalpy using the given densities.
First, convert the density of the liquid H2SO4 to grams per milliliter (g/mL):
1.83 g/mL
Next, calculate the mass of the liquid H2SO4:
Mass = Volume x Density
Mass = 1000 mL x 1.83 g/mL = 1830 g
Since 1 mole of H2SO4 has a molar mass of 98.09 g/mol, the number of moles in 1830 g of H2SO4 can be found:
Moles = Mass / Molar mass
Moles = 1830 g / 98.09 g/mol ≈ 18.67 mol
Now, let's consider the dilution process as an enthalpy change. At constant pressure, the enthalpy change (ÄH) is given by the equation:
ÄH = mcÄT
where m is the mass, c is the specific heat capacity, and ÄT is the change in temperature.
Since we are diluting 1.00 mol of H2SO4(l) to 1 L of 1.00 M H2SO4(aq), the mass of the solution (water + H2SO4) after dilution is equal to the mass of H2SO4 initially (1830 g).
Given:
Initial temperature (T1) = 28.8 °C
Final temperature (T2) = ?
Specific heat capacity (c) = 3.50 J/g·K
Change in temperature (ÄT) = T2 - T1
Now, substitute the given values into the enthalpy change equation:
ÄH = mcÄT
ÄH = (1830 g) x (3.50 J/g·K) x (T2 - 28.8 °C)
To find T2, we can rearrange the equation:
ÄH / (mc) = T2 - 28.8 °C
T2 = ÄH / (mc) + 28.8 °C
Substituting the ÄH value, which you labeled as -93.52 (Assuming this is correct), and the given specific heat capacity:
T2 = (-93.52 J) / [(1830 g) x (3.50 J/g·K)] + 28.8 °C
Calculating this expression will give you the final temperature, T2.
To find the enthalpy change (ΔHo) for diluting 1.00 mol of H2SO4(l) to 1 L of 1.00 M H2SO4(aq), we need to consider the density and molar mass of H2SO4.
Given:
Initial volume of H2SO4(l) = 1 L
Initial concentration of H2SO4(l) = 1.00 M
Final volume of H2SO4(aq) = 1 L
Final concentration of H2SO4(aq) = 1.00 M
Density of H2SO4(l) = 1.83 g/mL
Density of H2SO4(aq) = 1.060 g/mL
First, we need to calculate the initial and final masses of H2SO4.
Initial mass of H2SO4(l) = Initial volume × Density = 1 L × 1.83 g/mL = 1.83 g
Final mass of H2SO4(aq) = Final volume × Density = 1 L × 1.060 g/mL = 1.060 g
Next, we calculate the change in enthalpy using the formula:
ΔHo = q / n
where:
q = heat released or absorbed (in joules)
n = number of moles of H2SO4
In this case, we have 1.00 mol of H2SO4(l), so n = 1.00 mol.
We now need to calculate the heat released or absorbed during the dilution. We can use the equation:
q = m × c × ΔT
where:
m = mass (in grams)
c = specific heat capacity (in J/g·K)
ΔT = change in temperature (in °C)
Given:
Initial temperature (T1) = 28.8°C
Specific heat capacity of the final solution (c) = 3.50 J/g·K
We need to find the change in temperature, ΔT, to calculate the heat released or absorbed.
Assuming the dilution process is adiabatic (no heat exchange with the surroundings), we can equate the heat released during dilution to the heat absorbed by the final solution.
q released during dilution = q absorbed by the final solution
Using the equation q = m × c × ΔT, we can rewrite it as:
m₁ × c₁ × ΔT₁ = m₂ × c₂ × ΔT₂
where:
m₁ = initial mass of H2SO4(l)
c₁ = specific heat capacity of H2SO4(l)
ΔT₁ = change in temperature during dilution
m₂ = final mass of H2SO4(aq)
c₂ = specific heat capacity of the final solution
ΔT₂ = change in temperature of the final solution
Since the initial H2SO4(l) is at a higher concentration and heat release is highly exothermic, we can assume that the temperature of the dilution process is likely to increase. Therefore, ΔT₁ is positive.
Solving this equation for ΔT₂, we get:
ΔT₂ = (m₁ × c₁ × ΔT₁) / (m₂ × c₂)
Plugging in the given values:
m₁ = 1.83 g
c₁ = specific heat capacity of H2SO4(l) = ? (This value is required to proceed further.)
ΔT₁ = ? (This value is required to proceed further.)
m₂ = 1.060 g
c₂ = 3.50 J/g·K
Once we have the missing values, we can calculate ΔT₂ and then calculate the final temperature (Tf) using the equation:
Tf = T1 + ΔT₂
From the information provided in the question, it seems like some necessary values are missing, such as the specific heat capacity of H2SO4(l) and the change in temperature during dilution (ΔT₁). Without these values, we cannot determine the correct values of ΔH and the final temperature (Tf).