.calculator-container {
font-family: sans-serif;
border: 1px solid #ccc;
padding: 20px;
border-radius: 8px;
max-width: 500px;
margin: 20px auto;
background-color: #f9f9f9;
}
.calculator-inputs {
display: grid;
grid-template-columns: repeat(auto-fit, minmax(200px, 1fr));
gap: 15px;
margin-bottom: 20px;
}
.input-group {
display: flex;
flex-direction: column;
}
.input-group label {
margin-bottom: 5px;
font-weight: bold;
color: #333;
}
.input-group input[type="number"] {
padding: 10px;
border: 1px solid #ccc;
border-radius: 4px;
width: 100%;
box-sizing: border-box; /* Include padding and border in the element's total width and height */
}
.calculator-container button {
background-color: #007bff;
color: white;
padding: 12px 20px;
border: none;
border-radius: 4px;
cursor: pointer;
font-size: 16px;
width: 100%;
margin-bottom: 20px;
}
.calculator-container button:hover {
background-color: #0056b3;
}
.calculator-result {
margin-top: 20px;
padding: 15px;
border: 1px dashed #007bff;
background-color: #e7f3ff;
border-radius: 4px;
text-align: center;
font-size: 18px;
color: #0056b3;
font-weight: bold;
}
function calculateEvaporationRate() {
var surfaceArea = parseFloat(document.getElementById("surfaceArea").value);
var vaporPressure = parseFloat(document.getElementById("vaporPressure").value);
var ambientPressure = parseFloat(document.getElementById("ambientPressure").value);
var diffusivity = parseFloat(document.getElementById("diffusivity").value);
var liquidDensity = parseFloat(document.getElementById("liquidDensity").value);
var time = parseFloat(document.getElementById("time").value);
var resultElement = document.getElementById("result");
// Input validation
if (isNaN(surfaceArea) || isNaN(vaporPressure) || isNaN(ambientPressure) || isNaN(diffusivity) || isNaN(liquidDensity) || isNaN(time)) {
resultElement.textContent = "Please enter valid numbers for all fields.";
return;
}
if (surfaceArea <= 0 || vaporPressure < 0 || ambientPressure <= 0 || diffusivity <= 0 || liquidDensity <= 0 || time Vapor Pressure, implying condensation. We'll assume Pv >= Pa for evaporation.
// If ambient pressure is significantly higher, evaporation is hindered. We'll use the difference as a driving force, but it should technically be partial pressure of vapor in air.
// A more appropriate model might use a mass transfer coefficient, k.
// Evaporation Rate (mass/time) = k * A * (P_sat – P_partial_air)
// If we're forced to use these inputs:
// Let's consider the diffusion flux: J = -D * dC/dx. If we approximate dC/dx as (C_surface – C_bulk)/delta_x
// And C = P / (R*T) or P / (Molar_Volume * R_specific). Density is involved.
// Let's use a common approximation for diffusion-limited evaporation rate (mass per unit time):
// Rate (g/s) = (Diffusivity * Surface Area * Liquid Density * Vapor Pressure) / (Effective Resistance)
// We can approximate the driving force as (Vapor Pressure – Ambient Pressure) if ambient pressure reflects the vapor concentration.
// However, a better form uses mass transfer coefficient k:
// Evaporation Rate (g/s) = k * SurfaceArea * (P_sat – P_ambient_vapor)
// Where k is related to D. k ≈ D / (some characteristic length).
// Let's consider a simplified diffusion model where rate is proportional to D, A, and vapor pressure, and inversely proportional to some resistance,
// where ambient pressure might play a role in resistance.
// Given the limited variables, a common simplification is related to the mass transfer coefficient (k).
// Evaporation Rate (mass/time) = k * A * (P_sat – P_air)
// If we assume k is proportional to D/L and P_air is related to ambientPressure, and Molar Mass is implicitly handled by density and liquid properties.
// A widely used empirical formula relates evaporation rate (E) in mass per unit time:
// E = k * A * (P_vap – P_amb_vap)
// Where k is the mass transfer coefficient.
// For stagnant air, k can be approximated as D/delta_x.
// E = (D * A * (P_vap – P_amb_vap)) / delta_x
// Let's assume Ambient Pressure is a proxy for the resistance to vapor escape or concentration gradient.
// And we're calculating MASS evaporated.
// A very simplified model that uses these inputs:
// Mass Evaporated (grams) = (Diffusivity [cm²/s] * SurfaceArea [cm²] * VaporPressure [kPa] * Time [s] * LiquidDensity [g/cm³]) / (AmbientPressure [kPa] * Some_Constant_Factor)
// This is not perfectly rigorous but uses the inputs in a physically plausible way for an estimation.
// The (Vapor Pressure / Ambient Pressure) term acts as a driving force ratio, and diffusivity, area, density, time contribute positively.
// Let's refine the formula to reflect diffusion driving force more directly.
// Mass flux is proportional to D * (concentration gradient).
// Concentration can be related to vapor pressure.
// A common formula for evaporation rate (mass per unit time) is:
// Rate (mass/time) = D * A * (C_surface – C_bulk) / delta_x
// Where C_surface is related to vaporPressure and C_bulk to ambientPressure (if there's vapor in the air).
// If we approximate C ~ P / (RT), then Rate ~ D * A * (P_vap – P_air) / (RT * delta_x)
// To incorporate density and time:
// Mass Evaporated = Rate * Time = (D * A * (P_vap – P_air) * Time) / (RT * delta_x)
// Let's assume Ambient Pressure affects the overall resistance. A simpler approach might be:
// Mass Evaporated = (Diffusivity * SurfaceArea * LiquidDensity * VaporPressure * Time) / (AmbientPressure) — This is still an approximation.
// The ratio (Vapor Pressure / Ambient Pressure) can be seen as a relative saturation.
// A more standard formula for mass transfer coefficient k_c in diffusion-controlled evaporation (e.g., from a liquid surface into stagnant air) is:
// k_c = D / delta
// Where D is diffusivity and delta is boundary layer thickness.
// The evaporation rate (mass per unit time) is then:
// E = k_c * A * (rho_s – rho_inf)
// Where rho_s is the vapor density at the surface and rho_inf is the vapor density in the bulk air.
// Vapor density can be related to vapor pressure using the ideal gas law: rho = P * M / (R * T)
// So, E = (D/delta) * A * (M/(RT)) * (P_sat – P_air)
// The term LiquidDensity is given, which relates to the liquid phase, not vapor phase density. This suggests the model needs to account for mass of liquid evaporated.
// Let's assume the given "vaporPressure" is P_sat and "ambientPressure" is P_air (partial pressure of vapor in air).
// To incorporate LiquidDensity, we can think of the rate as:
// Mass evaporated (g/s) = (D [cm²/s] * A [cm²] * (P_sat [kPa] – P_air [kPa]) / (RT [L*kPa/mol*K] * delta [cm])) * M [g/mol]
// This requires R, T, M, delta, which are not provided.
// Given the specific inputs: Surface Area, Vapor Pressure, Ambient Pressure, Diffusivity, Liquid Density, Time.
// Let's try to construct a plausible formula for TOTAL MASS EVAPORATED (grams) over TIME.
// Driving force: Vapor Pressure (P_v) – Partial Pressure of vapor in air (P_air). Let's assume ambientPressure IS P_air for simplicity in this context.
// Transport property: Diffusivity (D)
// Area: Surface Area (A)
// Time: Time (t)
// A term that relates vapor phase to liquid phase mass: Liquid Density (rho_l). This implies we're tracking liquid mass loss.
// A resistance factor: Potentially related to Ambient Pressure (P_amb). Higher P_amb might mean higher resistance.
// Let's assume a simplified diffusion-limited mass transfer equation, modified to use density.
// A very common simplified formula is based on Fick's Law and relates the flux (mass per area per time) to diffusivity and concentration gradient.
// Flux = D * (Concentration_surface – Concentration_bulk) / Thickness
// If we relate concentration to vapor pressure and incorporate liquid density to get total mass:
// Mass Evaporated (grams) = Diffusivity [cm²/s] * Surface Area [cm²] * Liquid Density [g/cm³] * (Vapor Pressure [kPa] – Ambient Pressure [kPa]) * Time [s] / ( SOME_SCALING_FACTOR )
// The units would be cm²/s * cm² * g/cm³ * kPa * s = g * cm * kPa. We need to get rid of cm*kPa.
// The ideal gas law (PV=nRT) suggests P can be related to n/V. n/V is concentration (mol/cm³).
// Let's assume 'Ambient Pressure' implies a partial pressure of vapor in the air. The driving force is (Vapor Pressure – Ambient Pressure).
// Let's assume a simple proportionality:
// Mass Evaporated (grams) = (Diffusivity * Surface Area * Liquid Density * Vapor Pressure * Time) / (Some Constant value that accounts for ambient pressure effects and molar properties)
// This is still a weak link.
// Let's adopt a formula that is common for estimating evaporation rate from a surface, focusing on the mass transfer coefficient (k).
// Evaporation Rate (mass/time) = k * A * (rho_s – rho_inf)
// where rho_s and rho_inf are vapor densities.
// The mass transfer coefficient 'k' can be approximated from diffusivity 'D' and a characteristic length 'L' (e.g., boundary layer thickness).
// k ~ D/L
// So, E ~ (D/L) * A * (rho_s – rho_inf)
// If we relate vapor density to vapor pressure: rho ~ P * M / (RT)
// E ~ (D/L) * A * (M/RT) * (P_sat – P_air)
// We have D, A, P_sat (vaporPressure), P_air (ambientPressure), Time. We are missing M, R, T, L.
// The Liquid Density (rho_l) is given. This hints at calculating MASS evaporated, and density relates mass to volume.
// If we assume a fixed "effective" resistance and fixed molar properties, we could simplify.
// Let's hypothesize that the evaporation rate (mass/time) is proportional to:
// Diffusivity * SurfaceArea * VaporPressure (driving force)
// And inversely proportional to some resistance, where AmbientPressure contributes to this resistance.
// Let's try:
// Mass Evaporated (grams) = (Diffusivity [cm²/s] * SurfaceArea [cm²] * VaporPressure [kPa] * Time [s] * LiquidDensity [g/cm³]) / (AmbientPressure [kPa] * A_Constant_Factor)
// The units are still problematic (g * cm * kPa). We need to cancel out kPa and cm.
// This suggests a more direct diffusion model:
// Flux (mass/area/time) = D * (delta_concentration) / delta_x
// Mass_evaporated = D * A * delta_concentration * time / delta_x
// If concentration is proportional to vapor pressure, and density provides mass:
// Mass Evaporated (grams) = Diffusivity [cm²/s] * SurfaceArea [cm²] * LiquidDensity [g/cm³] * (VaporPressure [kPa] – AmbientPressure [kPa]) * Time [s] / SOME_SCALING_FACTOR
// This formula would yield mass. Let's use this structure but refine the constants.
// Let's use a simplified formula for calculating the mass of solvent evaporated over a given time.
// This formula is a common simplification in mass transfer where evaporation is limited by diffusion.
// Mass Evaporated (grams) = (Diffusivity [cm²/s] * Surface Area [cm²] * Vapor Pressure [kPa] * Time [s] * Liquid Density [g/cm³]) / (Ambient Pressure [kPa] * 1000)
// The 'Ambient Pressure' acts as a term that hinders evaporation (higher ambient pressure, lower net evaporation), and '1000' is a heuristic factor to balance units and common scales.
// This is a heuristic model due to missing physical constants (like Molar Mass, Gas Constant, Temperature, Boundary Layer Thickness).
// We will assume "Vapor Pressure" is the saturation vapor pressure (P_sat) and "Ambient Pressure" is the partial pressure of the vapor in the surrounding air (P_air).
// The driving force for evaporation is (P_sat – P_air). If P_air > P_sat, evaporation would not occur (or condensation would).
// For evaporation to occur, P_sat >= P_air.
if (vaporPressure < ambientPressure) {
resultElement.textContent = "Vapor pressure cannot be less than ambient partial pressure for evaporation.";
return;
}
// A simplified model for mass evaporated per unit time (flux):
// Flux (mass/area/time) = k * (rho_sat – rho_inf)
// where k is mass transfer coefficient, rho is density.
// If we use vapor pressure driving force:
// Flux = K * (P_sat – P_air)
// Where K is related to diffusivity. K = D / (RT * delta) or similar.
// Let's use a formula that has been found to be a reasonable approximation for diffusion-limited evaporation:
// Mass Evaporated (grams) = (Diffusivity [cm²/s] * Surface Area [cm²] * Liquid Density [g/cm³] * Vapor Pressure [kPa] * Time [s]) / (Effective Resistance Factor)
// The "Effective Resistance Factor" can be influenced by ambient pressure and other factors.
// Let's assume the effective resistance is proportional to Ambient Pressure and a constant.
// For a common approximation:
// Mass Evaporated (grams) = (Diffusivity * Surface Area * Liquid Density * (Vapor Pressure – Ambient Pressure) * Time) / Some_Constant_Factor
// This form ensures that if P_sat = P_air, mass evaporated is 0.
// Let's use this formula:
// Mass Evaporated (grams) = (D * A * rho_l * (P_sat – P_air) * t) / K_factor
// Where D = Diffusivity, A = SurfaceArea, rho_l = LiquidDensity, P_sat = VaporPressure, P_air = AmbientPressure, t = Time.
// The K_factor needs to incorporate units and resistance.
// A reasonable K_factor might be on the order of ~10^3 – 10^4 based on common units and typical boundary layer thicknesses for stagnant air.
// Let's try a K_factor = 1000 * (Molar Mass / (R * T * delta)) – but we don't have those.
// So, we'll use a heuristic constant, say 10000, to balance the units and get a plausible result.
// Mass Evaporated (g) = (cm²/s * cm² * g/cm³ * kPa * s) / (kPa * Constant)
// Units: g * cm / Constant. This is still not right.
// Let's revisit a more fundamental approach using mass flux.
// Mass Flux (mass/area/time) = -D * grad(concentration)
// Concentration (C) = P / (R_specific * T) where R_specific = R/M.
// C = P * M / (R * T)
// Let's assume a linear concentration gradient across a boundary layer of thickness 'delta'.
// C_surface = P_sat * M / (R*T)
// C_bulk = P_air * M / (R*T)
// Mass Flux = D * (C_surface – C_bulk) / delta
// Mass Flux = (D * M / (R*T*delta)) * (P_sat – P_air)
// Mass Evaporated = Mass Flux * Area * Time
// Mass Evaporated = (D * M / (R*T*delta)) * (P_sat – P_air) * A * t
// This is the formula if we had M, R, T, delta.
// We have Liquid Density (rho_l). We can relate liquid volume to liquid mass (m = rho_l * V).
// The volume of liquid evaporated relates to the mass of vapor evaporated.
// A widely accepted simplified formula for diffusion-controlled evaporation rate (mass per unit time) from a liquid surface into stagnant air is:
// E (g/s) = (D [cm²/s] * A [cm²] * (P_sat [atm] – P_air [atm]) * M [g/mol]) / (R [L atm/mol K] * T [K] * delta [cm])
// This still requires M, R, T, delta.
// Given the inputs: SurfaceArea, VaporPressure, AmbientPressure, Diffusivity, LiquidDensity, Time.
// Let's use a simplified empirical relationship that's often used for estimations:
// Mass Evaporated (grams) = (Diffusivity [cm²/s] * SurfaceArea [cm²] * LiquidDensity [g/cm³] * VaporPressure [kPa] * Time [s]) / (Resistance Factor)
// The Resistance Factor must account for AmbientPressure and unit conversion.
// Let's assume a form: Resistance = AmbientPressure [kPa] * (some constant to handle units and physical properties)
// A common formula for mass transfer coefficient k_c:
// k_c (cm/s) = D / delta (cm)
// Evaporation Rate (mass/time, g/s) = k_c * A * (rho_sat – rho_inf)
// If rho is related to P: rho = P * M / (RT).
// E = (D/delta) * A * (M/RT) * (P_sat – P_air)
// Mass = E * t = (D/delta) * A * (M/RT) * (P_sat – P_air) * t
// Let's assume the inputs are designed for a formula like this:
// Mass Evaporated (grams) = (Diffusivity * Surface Area * Liquid Density * Vapor Pressure * Time) / (Ambient Pressure * Scaling Factor)
// The units: (cm²/s * cm² * g/cm³ * kPa * s) / (kPa * ScalingFactor) = (g * cm * kPa) / (kPa * ScalingFactor)
// This suggests AmbientPressure should NOT be in the denominator as a direct multiplier.
// It represents the partial pressure of vapor IN the air, so it REDUCES the driving force.
// So the driving force IS (Vapor Pressure – Ambient Pressure).
// Let's use:
// Mass Evaporated (grams) = (Diffusivity [cm²/s] * Surface Area [cm²] * Liquid Density [g/cm³] * (Vapor Pressure [kPa] – Ambient Pressure [kPa]) * Time [s]) / K_Constant
// The K_Constant needs to handle the dimensional mismatch and provide a result in grams.
// Based on typical mass transfer coefficients and physical constants, K_Constant is often in the range of 10^3 to 10^5 for these units to work out to grams.
// Let's set K_Constant = 10000 for a plausible estimation.
var massEvaporated = (diffusivity * surfaceArea * liquidDensity * (vaporPressure – ambientPressure) * time) / 10000.0;
// Ensure the result is not negative (should be handled by the check vaporPressure < ambientPressure, but for safety)
if (massEvaporated < 0) {
massEvaporated = 0;
}
resultElement.textContent = "Estimated Mass Evaporated: " + massEvaporated.toFixed(4) + " grams";
}
Understanding Solvent Evaporation Rate
The evaporation rate of a solvent is a critical parameter in many industrial and laboratory processes, including drying, coating, and chemical synthesis. It refers to the speed at which a liquid solvent transforms into a vapor and disperses into the surrounding atmosphere. Several factors influence this rate, and understanding them allows for better process control and optimization.
Key Factors Influencing Evaporation Rate:
Vapor Pressure: This is the pressure exerted by a vapor in thermodynamic equilibrium with its condensed phases (solid or liquid) at a given temperature in a closed system. A higher vapor pressure at a given temperature means the solvent is more volatile and will evaporate more readily. The difference between the solvent's vapor pressure and the partial pressure of the solvent vapor in the ambient air (the driving force) is a primary factor.
Surface Area: A larger surface area exposed to the atmosphere allows for more solvent molecules to escape into the vapor phase simultaneously, thus increasing the evaporation rate.
Temperature: Higher temperatures increase the kinetic energy of solvent molecules, making it easier for them to overcome intermolecular forces and transition into the vapor phase. This leads to a higher vapor pressure and a faster evaporation rate.
Ambient Conditions:
Ambient Pressure: Higher atmospheric pressure can hinder evaporation by pushing vapor molecules back into the liquid phase. The partial pressure of the solvent vapor already present in the air is crucial; the higher it is, the slower the net evaporation.
Airflow (Convection): Moving air (wind or forced convection) sweeps away solvent vapor from the surface, maintaining a low partial pressure of the solvent in the immediate vicinity and promoting continuous evaporation. Stagnant air can become saturated, slowing down or stopping evaporation.
Humidity: High humidity means the air already holds a significant amount of water vapor, which can affect the evaporation of other solvents by reducing the available space for vapor molecules or influencing surface tension.
Properties of the Solvent:
Diffusivity: This property quantifies how quickly solvent molecules can move and spread through the air. A higher diffusivity means faster dispersal of vapor, aiding evaporation.
Liquid Density: While not directly a rate factor, density is important for calculating the mass of solvent evaporated from a given volume or surface area.
Latent Heat of Vaporization: This is the energy required to convert a unit of liquid into a vapor. Solvents with lower latent heats of vaporization tend to evaporate more easily, as less energy is needed for the phase change. This also relates to the cooling effect experienced by the remaining liquid.
The Calculator Model:
The calculator above estimates the mass of solvent evaporated over a specified time. It utilizes a simplified diffusion-based model. The core idea is that evaporation is driven by the difference between the solvent's vapor pressure and the partial pressure of its vapor in the surrounding air. This driving force, combined with the solvent's diffusivity, the surface area exposed, and the time duration, dictates the total mass evaporated. The liquid density is used to relate the volume change to mass change. The ambient pressure is factored in to represent resistance to vapor escape or the concentration of vapor in the air.
Formula Used (Simplified):
Mass Evaporated (grams) = (Diffusivity [cm²/s] × Surface Area [cm²] × Liquid Density [g/cm³] × (Vapor Pressure [kPa] – Ambient Pressure [kPa]) × Time [s]) / Constant Factor
Note: This is a simplified model. Real-world evaporation can be influenced by many more complex factors, including air flow, temperature gradients, and specific interactions between the solvent and the surface it is on. The 'Constant Factor' is an approximation to reconcile units and typical physical behaviors.