The instantaneous rate of reaction is the rate of a chemical reaction at a specific point in time. It's crucial for understanding how reaction speeds change as reactants are consumed and products are formed. Unlike the average rate of reaction, which is calculated over a time interval, the instantaneous rate provides a precise measure at a single moment.
To calculate the instantaneous rate of reaction, we need to know the change in concentration of a reactant or product over a very small change in time. Mathematically, this is represented as the derivative of the concentration with respect to time:
Rate = \( \frac{d[A]}{dt} \) or \( -\frac{d[B]}{dt} \)
Where:
\( [A] \) is the concentration of a reactant.
\( [B] \) is the concentration of a product.
\( t \) is time.
The negative sign for \( [B] \) is used because the concentration of a reactant decreases over time, while the concentration of a product increases.
In practice, for a smooth concentration vs. time curve, the instantaneous rate at a point can be found by determining the slope of the tangent line to the curve at that specific time point. For discrete data points, we often approximate the instantaneous rate by taking the average rate over a very small time interval around the point of interest.
This calculator approximates the instantaneous rate by calculating the average rate over a very small interval around a specified time, based on two data points.
function calculateReactionRate() {
var concentration1 = parseFloat(document.getElementById("concentration1").value);
var time1 = parseFloat(document.getElementById("time1").value);
var concentration2 = parseFloat(document.getElementById("concentration2").value);
var time2 = parseFloat(document.getElementById("time2").value);
var resultDiv = document.getElementById("result");
resultDiv.innerHTML = ""; // Clear previous results
if (isNaN(concentration1) || isNaN(time1) || isNaN(concentration2) || isNaN(time2)) {
resultDiv.innerHTML = "Please enter valid numbers for all fields.";
return;
}
if (time1 === time2) {
resultDiv.innerHTML = "Time 1 and Time 2 cannot be the same to calculate a rate. Please provide two distinct time points.";
return;
}
// Assuming concentration2 and time2 are later than concentration1 and time1
// If not, the rate will be negative, which is acceptable for reactant disappearance.
var deltaConcentration = concentration2 – concentration1;
var deltaTime = time2 – time1;
var instantaneousRate = deltaConcentration / deltaTime;
var displayRate;
var unit = "M/s";
var explanation = "";
// For simplicity in this calculator, we assume the input concentrations relate to a reactant
// If it were a product, deltaConcentration would be positive and rate positive.
// We'll display the magnitude and specify if it's a reactant or product rate.
if (instantaneousRate 0) {
displayRate = instantaneousRate;
explanation = "The calculated rate for the formation of a product is: ";
} else {
displayRate = 0;
explanation = "The calculated rate is zero. ";
}
resultDiv.innerHTML = "" + explanation + "" + displayRate.toFixed(5) + " " + unit + "";
}
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margin-bottom: 15px;
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