Ra + 2H_{2}SO_{4} → RaSO_{4} + 2H_{2}O + SO_{2}

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### Word Equation

Radium + Sulfuric Acid = Radium Sulfate + Water + Sulfur Dioxide

One mole of

and two moles of

react vĩ đại form one mole of

, two moles of

and one mole of

### Products

### Radium Sulfate - RaSO

_{4}### Water - H

_{2}O### Sulfur Dioxide - SO

_{2}Sulphur Dioxide R-764 Sulfurous Anhydride So2 Sulphur Dioxide , Sulfur Dioxide Sulfur Oxide Sulfurous Oxide Sulfurous Acid Anhydride SO2 Molar Mass SO2 Oxidation Number

### Thermodynamics

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

#### Is the Reaction Exothermic or Endothermic?

Ra (g) | 1 mol | 158.992 kJ/mol | -158.992 kJ |
---|---|---|---|

H_{2}SO_{4} (l) | 2 mol | -813.9972 kJ/mol | 1627.9944 kJ |

RaSO_{4} (s) | 1 mol | -1471.0944 kJ/mol | -1471.0944 kJ |

H_{2}O (g) | 2 mol | -241.818464 kJ/mol | -483.636928 kJ |

SO_{2} (g) | 1 mol | -296.829696 kJ/mol | -296.829696 kJ |

ΣΔH°_{f}(reactants) | -1469.0024 kJ | ||

ΣΔH°_{f}(products) | -2251.561024 kJ | ||

ΔH°_{rxn} | -782.558624 kJ |

ΣΔH°_{f}(reactants) > ΣΔH°_{f}(products), so sánh Ra + H2SO4 = RaSO4 + H2O + SO2 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.

Ra (g) | 1 mol | 176.3556 J/(mol K) | -176.3556 J/K |
---|---|---|---|

H_{2}SO_{4} (l) | 2 mol | 156.9 J/(mol K) | -313.8 J/K |

RaSO_{4} (s) | 1 mol | 138.072 J/(mol K) | 138.072 J/K |

H_{2}O (g) | 2 mol | 188.715136 J/(mol K) | 377.430272 J/K |

SO_{2} (g) | 1 mol | 248.1112 J/(mol K) | 248.1112 J/K |

ΣΔS°(reactants) | 490.1556 J/K | ||

ΣΔS°(products) | 763.613472 J/K | ||

ΔS°_{rxn} | 273.457872 J/K |

ΣΔS°(products) > ΣΔS°(reactants), so sánh Ra + H2SO4 = RaSO4 + H2O + SO2 is **endoentropic** (increase 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.

Ra (g) | 1 mol | 129.704 kJ/mol | -129.704 kJ |
---|---|---|---|

H_{2}SO_{4} (l) | 2 mol | -690.06712 kJ/mol | 1380.13424 kJ |

RaSO_{4} (s) | 1 mol | -1365.6576 kJ/mol | -1365.6576 kJ |

H_{2}O (g) | 2 mol | -228.588656 kJ/mol | -457.177312 kJ |

SO_{2} (g) | 1 mol | -300.193632 kJ/mol | -300.193632 kJ |

ΣΔG°(reactants) | -1250.43024 kJ | ||

ΣΔG°(products) | -2123.028544 kJ | ||

ΔG°_{rxn} | -872.598304 kJ |

ΣΔG°(reactants) > ΣΔG°(products), so sánh Ra + H2SO4 = RaSO4 + H2O + SO2 is **exergonic** (releases energy).

### Reaction Expressions

K_{c} or Q = ( [RaSO_{4}] [H_{2}O]^{2} [SO_{2}] ) / ( [Ra] [H_{2}SO_{4}]^{2} )

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

rate = -(Δ[Ra] / Δt) = -1/2 * (Δ[H_{2}SO_{4}] / Δt) = (Δ[RaSO_{4}] / Δt) = một nửa * (Δ[H_{2}O] / Δt) = (Δ[SO_{2}] / 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 vĩ đại 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

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## Balance Ra + H2SO4 = RaSO4 + H2O + SO2 Using the Algebraic Method

To balance the equation Ra + H2SO4 = RaSO4 + H2O + SO2 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 vĩ đại represent the unknown coefficients.

a Ra + b H

_{2}SO_{4}= c RaSO_{4}+ d H_{2}O + f SO_{2}### Create a System of Equations

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

**Ra**: 1a + 0b = 1c + 0d + 0f**H**: 0a + 2b = 0c + 2d + 0f**S**: 0a + 1b = 1c + 0d + 1f**O**: 0a + 4b = 4c + 1d + 2f### Solve For All Variables

Use substitution, Gaussian elimination, or a calculator vĩ đại solve for each variable.

- 1a - 1c = 0
- 2b - 2d = 0
- 1b - 1c - 1f = 0
- 4b - 4c - 1d - 2f = 0

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

[ 1 0 -1 0 0 0] [ 0 2 0 -2 0 0] [ 0 1 -1 0 -1 0] [ 0 4 -4 -1 -2 0]

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

Simplify the result vĩ đại get the lowest, whole integer values.

- a = 1 (Ra)
- b = 2 (H2SO4)
- c = 1 (RaSO4)
- d = 2 (H2O)
- f = 1 (SO2)

### 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.

Ra + 2 H

_{2}SO_{4}= RaSO_{4}+ 2 H_{2}O + SO_{2}Reactants Products Ra 1 1 ✔️ H 4 4 ✔️ S 2 2 ✔️ O 8 8 ✔️ Since there is an equal number of each element in the reactants and products of Ra + 2H2SO4 = RaSO4 + 2H2O + SO2, the equation is balanced.

## Balance Ra + H2SO4 = RaSO4 + H2O + SO2 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 kết thúc of a chemical reaction as at the beginning. To be balanced, every element in Ra + H2SO4 = RaSO4 + H2O + SO2 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 vĩ đại 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 | |||||||

Ra | H_{2}SO_{4} | Total | RaSO_{4} | H_{2}O | SO_{2} | Total | ||

Ra | 1 | 1 | 1 | 1 | ✔️ | |||

H | 2 | 2 | 2 | 2 | ✔️ | |||

S | 1 | 1 | 1 | 1 | 2 | ❌ | ||

O | 4 | 4 | 4 | 1 | 2 | 7 | ❌ |

### 2. Multiply coefficients for compounds vĩ đại balance out each element

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

**S**is not balanced. Add**1**molecule of**H**vĩ đại the reactant (left-hand) side vĩ đại balance Sulfur:_{2}SO_{4}

Ra + 2H_{2}SO_{4}= RaSO_{4}+ H_{2}O + SO_{2}Reactants Products Ra 1 1 ✔️ H 4 2 ❌ S 2 2 ✔️ O 8 7 ❌ **H**is not balanced. Add**1**molecule of**H**vĩ đại the product (right-hand) side vĩ đại balance Hydrogen:_{2}O

Ra + 2H_{2}SO_{4}= RaSO_{4}+ 2H_{2}O + SO_{2}Reactants Products Ra 1 1 ✔️ H 4 4 ✔️ S 2 2 ✔️ O 8 8 ✔️

### 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.

Ra + 2H_{2}SO_{4} = RaSO_{4} + 2H_{2}O + SO_{2}

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