Calculate the rate of reaction based on time measurements and estimate how temperature changes affect the reaction speed using the Arrhenius principles.
Typical range: 40-100 kJ/mol
Calculation Results
Initial Rate (at °C):–
Reaction Multiplier:–
Predicted Rate (at °C):–
Predicted Time (at °C):–
Note: This calculation uses the Arrhenius equation. Relative rate is calculated as 1/time (s⁻¹).
How to Calculate Rate of Reaction from Temperature and Time
In chemical kinetics, the rate of reaction is a measure of how quickly reactants turn into products. The most direct method to determine this rate in a laboratory setting involves measuring the time it takes for a specific event to occur (such as a color change or the disappearance of a solid) and noting the temperature.
1. Calculating Basic Rate from Time
If you measure the time ($t$) it takes for a reaction to complete (or reach a fixed point), the average rate is inversely proportional to time. The formula is:
Rate = 1 / Time
The unit for this relative rate is typically $s^{-1}$ (per second). For example, if a reaction takes 50 seconds to complete, the relative rate is $1 / 50 = 0.02 \, s^{-1}$.
2. The Effect of Temperature (Arrhenius Equation)
Temperature has a profound effect on the rate of reaction. As temperature increases, particles gain kinetic energy, leading to more frequent and energetic collisions. This relationship is mathematically described by the **Arrhenius Equation**.
To predict the rate at a new temperature, we compare the rate constants ($k_1$ and $k_2$) at temperatures $T_1$ and $T_2$ (in Kelvin):
ln(k₂/k₁) = (Eₐ / R) × (1/T₁ – 1/T₂)
Where:
k₁, k₂: Rate constants at temperatures T₁ and T₂.
Eₐ: Activation Energy (Joules/mol).
R: Universal Gas Constant (8.314 J/mol·K).
T: Temperature in Kelvin (°C + 273.15).
Example Calculation
Let's assume we are performing a "disappearing cross" experiment with sodium thiosulfate.
Initial State: The reaction takes 60 seconds at 20°C.
Goal: Estimate the time taken at 30°C.
Activation Energy (Assumption): Let's assume an $E_a$ of 50 kJ/mol (50,000 J/mol).
Step 2: Calculate Temperature Factor
Convert temperatures to Kelvin: $T_1 = 293K$, $T_2 = 303K$.
Using the Arrhenius formula, the rate roughly doubles for every 10°C rise (depending on $E_a$). With $E_a = 50\,kJ/mol$, the multiplier is approximately 1.97.
Step 3: New Rate and Time
New Rate ≈ $0.0167 \times 1.97 = 0.0329 \, s^{-1}$.
New Time = $1 / 0.0329 \approx 30.4$ seconds.
Frequently Asked Questions
Why do we calculate 1/time?
Since rate is "change in amount over time", and the "change in amount" is constant for a specific visual endpoint (like a cross disappearing), the rate is proportional to the reciprocal of time ($1/t$).
What is the Q10 rule?
The Q10 temperature coefficient is a rule of thumb stating that for many biological and chemical reactions, the rate of reaction doubles for every 10°C increase in temperature ($Q_{10} \approx 2$). This calculator uses the more precise Arrhenius equation, but the results are often similar.
Does Activation Energy change with temperature?
For most practical purposes in general chemistry, Activation Energy ($E_a$) is considered constant over small temperature ranges, although strictly speaking, it can vary slightly.
function calculateReaction() {
// 1. Get Input Elements
var timeInput = document.getElementById("initialTime");
var temp1Input = document.getElementById("initialTemp");
var temp2Input = document.getElementById("targetTemp");
var eaInput = document.getElementById("activEnergy");
var resultsDiv = document.getElementById("resultsArea");
// 2. Parse Values
var t1_seconds = parseFloat(timeInput.value);
var temp1_c = parseFloat(temp1Input.value);
var temp2_c = parseFloat(temp2Input.value);
var ea_kj = parseFloat(eaInput.value);
// 3. Validation
if (isNaN(t1_seconds) || t1_seconds <= 0) {
alert("Please enter a valid positive number for Time.");
return;
}
if (isNaN(temp1_c) || isNaN(temp2_c)) {
alert("Please enter valid temperatures.");
return;
}
if (isNaN(ea_kj) || ea_kj 0).");
return;
}
// 4. Constants
var R = 8.314; // Universal Gas Constant J/(mol*K)
// 5. Conversions
var temp1_k = temp1_c + 273.15;
var temp2_k = temp2_c + 273.15;
var ea_j = ea_kj * 1000; // Convert kJ to J
// 6. Calculate Initial Rate (Relative Rate = 1/t)
var rate1 = 1 / t1_seconds;
// 7. Calculate Arrhenius Multiplier (k2/k1)
// Formula: ln(k2/k1) = (Ea/R) * (1/T1 – 1/T2)
// Therefore: k2/k1 = exp( (Ea/R) * (1/T1 – 1/T2) )
var exponent = (ea_j / R) * ((1 / temp1_k) – (1 / temp2_k));
var multiplier = Math.exp(exponent);
// 8. Calculate New Rate and Time
var rate2 = rate1 * multiplier;
var t2_seconds = 1 / rate2;
// 9. Update UI with formatted results
document.getElementById("resInitTemp").innerText = temp1_c;
document.getElementById("resTargTemp").innerText = temp2_c;
document.getElementById("resTargTemp2").innerText = temp2_c;
document.getElementById("resInitRate").innerText = rate1.toExponential(4) + " s⁻¹";
document.getElementById("resMultiplier").innerText = multiplier.toFixed(2) + "x";
document.getElementById("resNewRate").innerText = rate2.toExponential(4) + " s⁻¹";
// Format time nicely
var timeDisplay = t2_seconds.toFixed(2) + " s";
if (t2_seconds < 0.01) {
timeDisplay = t2_seconds.toExponential(2) + " s";
}
document.getElementById("resNewTime").innerText = timeDisplay;
// Show results
resultsDiv.style.display = "block";
}