To calculate the mass of potassium nitrate required to absorb 107 kJ of heat, we can use the following formula:

```

q = mcΔT

```

Where:

- q is the heat absorbed (107 kJ)

- m is the mass of potassium nitrate

- c is the specific heat capacity of potassium nitrate (1.05 J/g°C)

- ΔT is the change in temperature (we can assume it's 1°C)

Substituting the given values into the formula:

```

107 kJ = m * 1.05 J/g°C * 1°C

```

```

m = 107 kJ / (1.05 J/g°C * 1°C)

```

```

m ≈ 102,381 g

```

Therefore, approximately 102,381 grams of potassium nitrate must dissolve in water to absorb 107 kJ of heat.