# Equilibrium pressure of calcium carbonate

• cheme2019
In summary, at equilibrium, calcium carbonate will be present as two crystalline phases - calcite and aragonite - at a pressure of 3850.9 cm^3.
cheme2019

## Homework Statement

Calcium carbonate primarily occurs as two crystalline forms, calcite and aragonite. The value of∆!° for the transition
CaCO3(calcite) ⇌ CaCO3(aragonite)
is +1.04 kJ·mol-1 at 25°C. At that temperature the density for calcite is 2.710 g·cm-3, and that of aragonite is 2.930 g·cm-3. At what pressure will the two crystalline phases be at equilibrium at 25°C?

## Homework Equations

ln(ai)= ((molar V)/RT) * (P-1)
ΔG = -RT * ln(Kp
Kp = aaragonite/acalcite

## The Attempt at a Solution

So I started by finding the molar volume of each by dividing the MW by the individual density and got
Vara = 34.157 cm^3/mol and
Vcal = 36.930 cm^3/ mol
From here I used the activity equation to get that

ai = e^(((molar V)/RT) * (P-1)))

And since

Kp = aaragonite/acalcite and
ΔG = -RT * ln(Kp

I can write that

ΔG = -RT * ln(aaragonite/acalcite)

ΔG = -RT * (((molar Vara/RT) * (P-1) - ((molar Vcal/RT)*(P-1))
Or
ΔG = - molar Vara*(P-1)+(molar Vcal*(P-1))

Continuing
1040 J/mol =(-34.157 cm^3/mol ) * P + 34.157 cm^3/mol +(36.930 cm^3/mol) * P - 39.630 cm^3/mol

Solving for P I get 376 J/cm^3.
I am given that the answer is 3850.9 but no units and I wasn't able to convert my units to get that number...
I'm pretty sure my math is correct but I think I messed up on units somewhere. Any help would be greatly appreciated! Thanks!

Step one: pick CGS or MKS; do not attempt to mix them when you're not comfortable with either; i.e., densities are expressed as kg/m3 in MKS, and as g/cm3 in CGS; pressures in force per unit area, not energy per unit volume ...

But can't you use energy per unit volume for pressure? Similar to how atm is J/L. Plus I'm only given ΔG in kJ/mol and I don't know how to convert that into CGS

Atm is not J/L; 1 J/L = 1000 Pa; 1 atm = 101325 Pa

## 1. What is the equilibrium pressure of calcium carbonate?

The equilibrium pressure of calcium carbonate is the pressure at which the rates of the forward and reverse reactions of the calcium carbonate equilibrium are equal. This means that at this pressure, the amount of calcium carbonate that dissolves in water is equal to the amount that precipitates out of the solution.

## 2. How is the equilibrium pressure of calcium carbonate determined?

The equilibrium pressure of calcium carbonate is determined through experiments that measure the amount of calcium carbonate dissolved in water at different pressures. The data is then used to plot a graph, and the equilibrium pressure is where the two lines representing the forward and reverse reactions intersect.

## 3. What factors affect the equilibrium pressure of calcium carbonate?

The factors that affect the equilibrium pressure of calcium carbonate include temperature, pressure, and the concentration of calcium and carbonate ions in the solution. Higher temperatures and pressures generally lead to a higher equilibrium pressure, while higher concentrations of calcium and carbonate ions can shift the equilibrium towards the formation of more calcium carbonate.

## 4. Why is the equilibrium pressure of calcium carbonate important?

The equilibrium pressure of calcium carbonate is important because it determines the solubility of calcium carbonate in water. This is significant in many industries, such as water treatment, cement production, and agriculture, where the presence of calcium carbonate can have a significant impact on the quality of the final product.

## 5. Can the equilibrium pressure of calcium carbonate be changed?

Yes, the equilibrium pressure of calcium carbonate can be changed by altering the factors that affect it, such as temperature, pressure, and ion concentrations. For example, increasing the temperature or pressure will shift the equilibrium towards the formation of more calcium carbonate, while increasing the concentration of calcium or carbonate ions will shift the equilibrium in the opposite direction.

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