3C + CaO → CaC_{2} + CO

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### Word Equation

Carbon + Calcium Oxide = Calcium Carbide + Carbon Monoxide

Three moles of

and one mole of

react đồ sộ form one mole of

and one mole of

### Thermodynamics

Thermodynamics of the reaction can be calculated using a lookup table.

#### Is the Reaction Exothermic or Endothermic?

C (g) | 3 mol | 716.681544 kJ/mol | -2150.044632 kJ |
---|---|---|---|

CaO (s) | 1 mol | -635.1312 kJ/mol | 635.1312 kJ |

CaC_{2} (s) | 1 mol | -59.8312 kJ/mol | -59.8312 kJ |

CO (g) | 1 mol | -110.54128 kJ/mol | -110.54128 kJ |

ΣΔH°_{f}(reactants) | 1514.913432 kJ | ||

ΣΔH°_{f}(products) | -170.37248 kJ | ||

ΔH°_{rxn} | -1685.285912 kJ |

ΣΔH°_{f}(reactants) > ΣΔH°_{f}(products), ví C + CaO = CaC2 + CO is **exothermic** (releases heat).

#### Is the Reaction Exoentropic or Endoentropic?

ΔS = S_{products} - S_{reactants}. If ΔS < 0, it is exoentropic. If ΔS > 0, it is endoentropic.

C (g) | 3 mol | 157.9865848 J/(mol K) | -473.9597544 J/K |
---|---|---|---|

CaO (s) | 1 mol | 38.19992 J/(mol K) | -38.19992 J/K |

CaC_{2} (s) | 1 mol | 69.95648 J/(mol K) | 69.95648 J/K |

CO (g) | 1 mol | 197.9032 J/(mol K) | 197.9032 J/K |

ΣΔS°(reactants) | 512.1596744 J/K | ||

ΣΔS°(products) | 267.85968 J/K | ||

ΔS°_{rxn} | -244.2999944 J/K |

ΣΔS°(reactants) > ΣΔS°(products), ví C + CaO = CaC2 + CO is **exoentropic** (decrease in entropy).

#### Is the Reaction Exergonic or Endergonic?

ΔG = G_{products} - G_{reactants}. If ΔG < 0, it is exergonic. If ΔG > 0, it is endergonic.

C (g) | 3 mol | 671.289328 kJ/mol | -2013.867984 kJ |
---|---|---|---|

CaO (s) | 1 mol | -603.542 kJ/mol | 603.542 kJ |

CaC_{2} (s) | 1 mol | -64.852 kJ/mol | -64.852 kJ |

CO (g) | 1 mol | -137.27704 kJ/mol | -137.27704 kJ |

ΣΔG°(reactants) | 1410.325984 kJ | ||

ΣΔG°(products) | -202.12904 kJ | ||

ΔG°_{rxn} | -1612.455024 kJ |

ΣΔG°(reactants) > ΣΔG°(products), ví C + CaO = CaC2 + CO is **exergonic** (releases energy).

### Reaction Expressions

K_{c} or Q = ( [CaC_{2}] [CO] ) / ( [C]^{3} [CaO] )

(assuming all reactants and products are aqueous. substitutue 1 for any solids/liquids, and Psubstance for gases.)

rate = -1/3 * (Δ[C] / Δt) = -(Δ[CaO] / Δt) = (Δ[CaC_{2}] / Δt) = (Δ[CO] / Δt)

(assuming constant volume in a closed system and no accumulation of intermediates or side products)

## Instructions

To balance a chemical equation, enter an equation of a chemical reaction and press the Balance button. The balanced equation will appear above.

- Use uppercase for the first character in the element and lowercase for the second character. Examples: Fe, Au, Co, Br, C, O, N, F.
- Ionic charges are not yet supported and will be ignored.
- Replace immutable groups in compounds đồ sộ avoid ambiguity. For example, C6H5C2H5 + O2 = C6H5OH + CO2 + H2O will not be balanced, but XC2H5 + O2 = XOH + CO2 + H2O will.
- Compound states [like (s) (aq) or (g)] are not required.
- You can use parenthesis () or brackets [].

## How To Balance Equations

Read our article on how đồ sộ balance chemical equations or ask for help in our chat.

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## Balance C + CaO = CaC2 + CO Using the Algebraic Method

To balance the equation C + CaO = CaC2 + CO using the algebraic method step-by-step, you must have experience solving systems of linear equations. The most common methods are substitution/elimination and linear algebra, but any similar method will work.

### Label Each Compound With a Variable

Label each compound (reactant or product) in the equation with a variable đồ sộ represent the unknown coefficients.

a C + b CaO = c CaC

_{2}+ d CO### Create a System of Equations

Create an equation for each element (C, Ca, O) where each term represents the number of atoms of the element in each reactant or product.

**C**: 1a + 0b = 2c + 1d**Ca**: 0a + 1b = 1c + 0d**O**: 0a + 1b = 0c + 1d### Solve For All Variables

Use substitution, Gaussian elimination, or a calculator đồ sộ solve for each variable.

- 1a - 2c - 1d = 0
- 1b - 1c = 0
- 1b - 1d = 0

Use your graphing calculator's rref() function (or an online rref calculator) đồ sộ convert the following matrix into reduced row-echelon-form:

[ 1 0 -2 -1 0] [ 0 1 -1 0 0] [ 0 1 0 -1 0]

The resulting matrix can be used đồ sộ determine the coefficients. In the case of a single solution, the last column of the matrix will contain the coefficients.

Simplify the result đồ sộ get the lowest, whole integer values.

- a = 3 (C)
- b = 1 (CaO)
- c = 1 (CaC2)
- d = 1 (CO)

### Substitute Coefficients and Verify Result

Count the number of atoms of each element on each side of the equation and verify that all elements and electrons (if there are charges/ions) are balanced.

3 C + CaO = CaC

_{2}+ COReactants Products C 3 3 ✔️ Ca 1 1 ✔️ O 1 1 ✔️ Since there is an equal number of each element in the reactants and products of 3C + CaO = CaC2 + CO, the equation is balanced.

## Balance C + CaO = CaC2 + CO Using Inspection

The law of conservation of mass states that matter cannot be created or destroyed, which means there must be the same number atoms at the over of a chemical reaction as at the beginning. To be balanced, every element in C + CaO = CaC2 + CO must have the same number of atoms on each side of the equation. When using the inspection method (also known as the trial-and-error method), this principle is used đồ sộ balance one element at a time until both sides are equal and the chemical equation is balanced.

### 1. Count the number of each element on the left and right hand sides

Reactants (Left Hand Side) | Products (Right Hand Side) | ||||||
---|---|---|---|---|---|---|---|

Reactants | Products | ||||||

C | CaO | Total | CaC_{2} | CO | Total | ||

C | 1 | 1 | 2 | 1 | 3 | ❌ | |

Ca | 1 | 1 | 1 | 1 | ✔️ | ||

O | 1 | 1 | 1 | 1 | ✔️ |

### 2. Multiply coefficients for compounds đồ sộ balance out each element

For each element that is not equal, try đồ sộ balance it by adding more of it đồ sộ the side with less. Sometimes there may be multiple compounds with that element on one side, ví you'll need đồ sộ use your best judgement and be prepared đồ sộ go back and try the other options.

**C**is not balanced. Add**2**molecules of**C**đồ sộ the reactant (left-hand) side đồ sộ balance Carbon:

3C + CaO = CaC_{2}+ COReactants Products C 3 3 ✔️ Ca 1 1 ✔️ O 1 1 ✔️

### 3. Verify that the equation is balanced

Since there are an equal number of atoms of each element on both sides, the equation is balanced.

3C + CaO = CaC_{2} + CO

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