Update src/streamlit_app.py

src/streamlit_app.py

@@ -2,98 +2,208 @@ import streamlit as st
 import pandas as pd
 import math
 
+# 语言配置
+LANGUAGES = {
+    "中文": {
+        "page_title": "溶剂分数转换器",
+        "main_title": "🧪 溶剂摩尔分数与体积分数转换器",
+        "conversion_mode": "转换模式",
+        "mode_mole_to_vol": "摩尔分数 → 体积分数",
+        "mode_vol_to_mole": "体积分数 → 摩尔分数",
+        "select_conversion": "选择转换方向:",
+        "solvent_selection": "溶剂选择",
+        "select_solvents": "选择两种溶剂或自定义参数:",
+        "solvent_a": "溶剂A:",
+        "solvent_b": "溶剂B:",
+        "custom": "自定义",
+        "molar_mass": "摩尔质量",
+        "density": "密度",
+        "input_mole_fraction": "输入摩尔分数",
+        "input_volume_fraction": "输入体积分数",
+        "mole_fraction_of": "的摩尔分数",
+        "volume_fraction_of": "的体积分数",
+        "result_volume_fraction": "计算结果 - 体积分数",
+        "result_mole_fraction": "计算结果 - 摩尔分数",
+        "verification": "验证",
+        "detailed_info": "详细信息",
+        "solvent_params": "溶剂参数",
+        "solvent": "溶剂",
+        "mole_fraction": "摩尔分数",
+        "volume_fraction": "体积分数",
+        "calculation_formula": "计算公式",
+        "formula_mole_to_vol_title": "**摩尔分数转换为体积分数:**",
+        "formula_vol_to_mole_title": "**体积分数转换为摩尔分数:**",
+        "formula_where": "其中:",
+        "usage_instructions": "使用说明",
+        "instruction_1": "1. **选择转换模式**: 在侧边栏选择转换方向",
+        "instruction_2": "2. **选择溶剂**: 从预设的常见溶剂中选择，或选择\"自定义\"输入参数",
+        "instruction_3": "3. **输入数值**: 使用滑块调整摩尔分数或体积分数",
+        "instruction_4": "4. **查看结果**: 右侧显示转换结果和详细信息",
+        "note": "**注意**: 本计算假设理想混合，实际情况可能存在偏差。",
+        "language": "语言"
+    },
+    "English": {
+        "page_title": "Solvent Fraction Converter",
+        "main_title": "🧪 Solvent Mole Fraction & Volume Fraction Converter",
+        "conversion_mode": "Conversion Mode",
+        "mode_mole_to_vol": "Mole Fraction → Volume Fraction",
+        "mode_vol_to_mole": "Volume Fraction → Mole Fraction",
+        "select_conversion": "Select conversion direction:",
+        "solvent_selection": "Solvent Selection",
+        "select_solvents": "Select two solvents or customize parameters:",
+        "solvent_a": "Solvent A:",
+        "solvent_b": "Solvent B:",
+        "custom": "Custom",
+        "molar_mass": "Molar Mass",
+        "density": "Density",
+        "input_mole_fraction": "Input Mole Fraction",
+        "input_volume_fraction": "Input Volume Fraction",
+        "mole_fraction_of": "Mole fraction of",
+        "volume_fraction_of": "Volume fraction of",
+        "result_volume_fraction": "Results - Volume Fraction",
+        "result_mole_fraction": "Results - Mole Fraction",
+        "verification": "Verification",
+        "detailed_info": "Detailed Information",
+        "solvent_params": "Solvent Parameters",
+        "solvent": "Solvent",
+        "mole_fraction": "Mole Fraction",
+        "volume_fraction": "Volume Fraction",
+        "calculation_formula": "Calculation Formula",
+        "formula_mole_to_vol_title": "**Mole Fraction to Volume Fraction:**",
+        "formula_vol_to_mole_title": "**Volume Fraction to Mole Fraction:**",
+        "formula_where": "Where:",
+        "usage_instructions": "Usage Instructions",
+        "instruction_1": "1. **Select Conversion Mode**: Choose conversion direction in sidebar",
+        "instruction_2": "2. **Select Solvents**: Choose from preset common solvents or select 'Custom' to input parameters",
+        "instruction_3": "3. **Input Values**: Use sliders to adjust mole fraction or volume fraction",
+        "instruction_4": "4. **View Results**: Results and detailed information are displayed on the right",
+        "note": "**Note**: This calculation assumes ideal mixing; actual situations may deviate.",
+        "language": "Language"
+    }
+}
+
+# 常见溶剂的摩尔质量和密度数据库（中英文对照）
+SOLVENTS_DB = {
+    "中文": {
+        "水": {"M": 18.02, "density": 1.000, "en": "Water"},
+        "乙醇": {"M": 46.07, "density": 0.789, "en": "Ethanol"},
+        "甲醇": {"M": 32.04, "density": 0.792, "en": "Methanol"},
+        "异丙醇": {"M": 60.10, "density": 0.786, "en": "Isopropanol"},
+        "丙酮": {"M": 58.08, "density": 0.784, "en": "Acetone"},
+        "乙酸乙酯": {"M": 88.11, "density": 0.902, "en": "Ethyl Acetate"},
+        "甲苯": {"M": 92.14, "density": 0.867, "en": "Toluene"},
+        "二氯甲烷": {"M": 84.93, "density": 1.326, "en": "Dichloromethane"},
+        "氯仿": {"M": 119.38, "density": 1.489, "en": "Chloroform"},
+        "四氢呋喃": {"M": 72.11, "density": 0.889, "en": "Tetrahydrofuran"},
+        "二甲基亚砜": {"M": 78.13, "density": 1.100, "en": "Dimethyl Sulfoxide"},
+        "N,N-二甲基甲酰胺": {"M": 73.09, "density": 0.944, "en": "N,N-Dimethylformamide"},
+        "乙腈": {"M": 41.05, "density": 0.786, "en": "Acetonitrile"},
+        "正己烷": {"M": 86.18, "density": 0.659, "en": "n-Hexane"},
+        "环己烷": {"M": 84.16, "density": 0.779, "en": "Cyclohexane"},
+        "苯": {"M": 78.11, "density": 0.876, "en": "Benzene"},
+        "乙二醇": {"M": 62.07, "density": 1.113, "en": "Ethylene Glycol"},
+        "甘油": {"M": 92.09, "density": 1.261, "en": "Glycerol"}
+    },
+    "English": {
+        "Water": {"M": 18.02, "density": 1.000, "cn": "水"},
+        "Ethanol": {"M": 46.07, "density": 0.789, "cn": "乙醇"},
+        "Methanol": {"M": 32.04, "density": 0.792, "cn": "甲醇"},
+        "Isopropanol": {"M": 60.10, "density": 0.786, "cn": "异丙醇"},
+        "Acetone": {"M": 58.08, "density": 0.784, "cn": "丙酮"},
+        "Ethyl Acetate": {"M": 88.11, "density": 0.902, "cn": "乙酸乙酯"},
+        "Toluene": {"M": 92.14, "density": 0.867, "cn": "甲苯"},
+        "Dichloromethane": {"M": 84.93, "density": 1.326, "cn": "二氯甲烷"},
+        "Chloroform": {"M": 119.38, "density": 1.489, "cn": "氯仿"},
+        "Tetrahydrofuran": {"M": 72.11, "density": 0.889, "cn": "四氢呋喃"},
+        "Dimethyl Sulfoxide": {"M": 78.13, "density": 1.100, "cn": "二甲基亚砜"},
+        "N,N-Dimethylformamide": {"M": 73.09, "density": 0.944, "cn": "N,N-二甲基甲酰胺"},
+        "Acetonitrile": {"M": 41.05, "density": 0.786, "cn": "乙腈"},
+        "n-Hexane": {"M": 86.18, "density": 0.659, "cn": "正己烷"},
+        "Cyclohexane": {"M": 84.16, "density": 0.779, "cn": "环己烷"},
+        "Benzene": {"M": 78.11, "density": 0.876, "cn": "苯"},
+        "Ethylene Glycol": {"M": 62.07, "density": 1.113, "cn": "乙二醇"},
+        "Glycerol": {"M": 92.09, "density": 1.261, "cn": "甘油"}
+    }
+}
+
+# 语言选择
+language = st.sidebar.selectbox("Language/语言:", ["中文", "English"])
+lang = LANGUAGES[language]
+
 # 配置页面
 st.set_page_config(
-    page_title="溶剂分数转换器",
+    page_title=lang["page_title"],
     page_icon="🧪",
     layout="wide"
 )
 
 # 页面标题
-st.title("🧪 溶剂摩尔分数与体积分数转换器")
+st.title(lang["main_title"])
 st.markdown("---")
 
-# 常见溶剂的摩尔质量和密度数据库
-SOLVENTS_DB = {
-    "水": {"M": 18.02, "density": 1.000},
-    "乙醇": {"M": 46.07, "density": 0.789},
-    "甲醇": {"M": 32.04, "density": 0.792},
-    "异丙醇": {"M": 60.10, "density": 0.786},
-    "丙酮": {"M": 58.08, "density": 0.784},
-    "乙酸乙酯": {"M": 88.11, "density": 0.902},
-    "甲苯": {"M": 92.14, "density": 0.867},
-    "二氯甲烷": {"M": 84.93, "density": 1.326},
-    "氯仿": {"M": 119.38, "density": 1.489},
-    "四氢呋喃": {"M": 72.11, "density": 0.889},
-    "二甲基亚砜": {"M": 78.13, "density": 1.100},
-    "N,N-二甲基甲酰胺": {"M": 73.09, "density": 0.944},
-    "乙腈": {"M": 41.05, "density": 0.786},
-    "正己烷": {"M": 86.18, "density": 0.659},
-    "环己烷": {"M": 84.16, "density": 0.779},
-    "苯": {"M": 78.11, "density": 0.876},
-    "乙二醇": {"M": 62.07, "density": 1.113},
-    "甘油": {"M": 92.09, "density": 1.261}
-}
-
 # 侧边栏 - 转换模式选择
-st.sidebar.header("转换模式")
+st.sidebar.header(lang["conversion_mode"])
 conversion_mode = st.sidebar.radio(
-    "选择转换方向:",
-    ["摩尔分数 → 体积分数", "体积分数 → 摩尔分数"]
+    lang["select_conversion"],
+    [lang["mode_mole_to_vol"], lang["mode_vol_to_mole"]]
 )
 
 # 溶剂选择
-st.sidebar.header("溶剂选择")
-st.sidebar.write("选择两种溶剂或自定义参数:")
+st.sidebar.header(lang["solvent_selection"])
+st.sidebar.write(lang["select_solvents"])
+
+# 获取当前语言的溶剂列表
+current_solvents = SOLVENTS_DB[language]
+solvent_names = list(current_solvents.keys()) + [lang["custom"]]
 
 # 溶剂A选择
-solvent_a_name = st.sidebar.selectbox("溶剂A:", list(SOLVENTS_DB.keys()) + ["自定义"])
+solvent_a_name = st.sidebar.selectbox(lang["solvent_a"], solvent_names)
 
-if solvent_a_name == "自定义":
+if solvent_a_name == lang["custom"]:
     col1, col2 = st.sidebar.columns(2)
     with col1:
-        M_a = st.number_input("摩尔质量A (g/mol):", value=18.02, min_value=0.1, step=0.01)
+        M_a = st.number_input(f"{lang['molar_mass']} A (g/mol):", value=18.02, min_value=0.1, step=0.01)
     with col2:
-        rho_a = st.number_input("密度A (g/cm³):", value=1.000, min_value=0.1, step=0.001)
+        rho_a = st.number_input(f"{lang['density']} A (g/cm³):", value=1.000, min_value=0.1, step=0.001)
 else:
-    M_a = SOLVENTS_DB[solvent_a_name]["M"]
-    rho_a = SOLVENTS_DB[solvent_a_name]["density"]
-    st.sidebar.write(f"摩尔质量: {M_a} g/mol")
-    st.sidebar.write(f"密度: {rho_a} g/cm³")
+    M_a = current_solvents[solvent_a_name]["M"]
+    rho_a = current_solvents[solvent_a_name]["density"]
+    st.sidebar.write(f"{lang['molar_mass']}: {M_a} g/mol")
+    st.sidebar.write(f"{lang['density']}: {rho_a} g/cm³")
 
 # 溶剂B选择
-solvent_b_name = st.sidebar.selectbox("溶剂B:", list(SOLVENTS_DB.keys()) + ["自定义"])
+solvent_b_name = st.sidebar.selectbox(lang["solvent_b"], solvent_names)
 
-if solvent_b_name == "自定义":
+if solvent_b_name == lang["custom"]:
     col1, col2 = st.sidebar.columns(2)
     with col1:
-        M_b = st.number_input("摩尔质量B (g/mol):", value=46.07, min_value=0.1, step=0.01)
+        M_b = st.number_input(f"{lang['molar_mass']} B (g/mol):", value=46.07, min_value=0.1, step=0.01)
     with col2:
-        rho_b = st.number_input("密度B (g/cm³):", value=0.789, min_value=0.1, step=0.001)
+        rho_b = st.number_input(f"{lang['density']} B (g/cm³):", value=0.789, min_value=0.1, step=0.001)
 else:
-    M_b = SOLVENTS_DB[solvent_b_name]["M"]
-    rho_b = SOLVENTS_DB[solvent_b_name]["density"]
-    st.sidebar.write(f"摩尔质量: {M_b} g/mol")
-    st.sidebar.write(f"密度: {rho_b} g/cm³")
+    M_b = current_solvents[solvent_b_name]["M"]
+    rho_b = current_solvents[solvent_b_name]["density"]
+    st.sidebar.write(f"{lang['molar_mass']}: {M_b} g/mol")
+    st.sidebar.write(f"{lang['density']}: {rho_b} g/cm³")
 
 # 主界面内容
 col1, col2 = st.columns(2)
 
-if conversion_mode == "摩尔分数 → 体积分数":
+if conversion_mode == lang["mode_mole_to_vol"]:
     with col1:
-        st.header("输入摩尔分数")
-        x_a = st.slider(
-            f"{solvent_a_name}的摩尔分数 (x_A):",
+        st.header(lang["input_mole_fraction"])
+        x_a = st.number_input(
+            f"{lang['mole_fraction_of']} {solvent_a_name} (x_A):",
             min_value=0.0,
             max_value=1.0,
             value=0.5,
-            step=0.01
+            step=0.001,
+            format="%.4f"
         )
         x_b = 1.0 - x_a
-        st.write(f"{solvent_b_name}的摩尔分数 (x_B): {x_b:.3f}")
+        st.write(f"{lang['mole_fraction_of']} {solvent_b_name} (x_B): {x_b:.4f}")
         
         # 计算体积分数
-        # V_A/V_total = (x_A * M_A / rho_A) / (x_A * M_A / rho_A + x_B * M_B / rho_B)
         V_ratio_a = x_a * M_a / rho_a
         V_ratio_b = x_b * M_b / rho_b
         V_total = V_ratio_a + V_ratio_b
@@ -105,28 +215,28 @@ if conversion_mode == "摩尔分数 → 体积分数":
             phi_a = phi_b = 0
         
     with col2:
-        st.header("计算结果 - 体积分数")
-        st.metric(f"{solvent_a_name}的体积分数 (φ_A)", f"{phi_a:.4f}")
-        st.metric(f"{solvent_b_name}的体积分数 (φ_B)", f"{phi_b:.4f}")
+        st.header(lang["result_volume_fraction"])
+        st.metric(f"{lang['volume_fraction_of']} {solvent_a_name} (φ_A)", f"{phi_a:.4f}")
+        st.metric(f"{lang['volume_fraction_of']} {solvent_b_name} (φ_B)", f"{phi_b:.4f}")
         
         # 验证
-        st.write(f"验证: φ_A + φ_B = {phi_a + phi_b:.4f}")
+        st.write(f"{lang['verification']}: φ_A + φ_B = {phi_a + phi_b:.4f}")
 
 else:  # 体积分数 → 摩尔分数
     with col1:
-        st.header("输入体积分数")
-        phi_a = st.slider(
-            f"{solvent_a_name}的体积分数 (φ_A):",
+        st.header(lang["input_volume_fraction"])
+        phi_a = st.number_input(
+            f"{lang['volume_fraction_of']} {solvent_a_name} (φ_A):",
             min_value=0.0,
             max_value=1.0,
             value=0.5,
-            step=0.01
+            step=0.001,
+            format="%.4f"
         )
         phi_b = 1.0 - phi_a
-        st.write(f"{solvent_b_name}的体积分数 (φ_B): {phi_b:.3f}")
+        st.write(f"{lang['volume_fraction_of']} {solvent_b_name} (φ_B): {phi_b:.4f}")
         
         # 计算摩尔分数
-        # x_A = (phi_A * rho_A / M_A) / (phi_A * rho_A / M_A + phi_B * rho_B / M_B)
         n_ratio_a = phi_a * rho_a / M_a
         n_ratio_b = phi_b * rho_b / M_b
         n_total = n_ratio_a + n_ratio_b
@@ -138,101 +248,131 @@ else:  # 体积分数 → 摩尔分数
             x_a = x_b = 0
         
     with col2:
-        st.header("计算结果 - 摩尔分数")
-        st.metric(f"{solvent_a_name}的摩尔分数 (x_A)", f"{x_a:.4f}")
-        st.metric(f"{solvent_b_name}的摩尔分数 (x_B)", f"{x_b:.4f}")
+        st.header(lang["result_mole_fraction"])
+        st.metric(f"{lang['mole_fraction_of']} {solvent_a_name} (x_A)", f"{x_a:.4f}")
+        st.metric(f"{lang['mole_fraction_of']} {solvent_b_name} (x_B)", f"{x_b:.4f}")
         
         # 验证
-        st.write(f"验证: x_A + x_B = {x_a + x_b:.4f}")
-
+        st.write(f"{lang['verification']}: x_A + x_B = {x_a + x_b:.4f}")
+        
 # 详细信息展示
 st.markdown("---")
-st.header("详细信息")
+st.header(lang["detailed_info"])
 
 col1, col2, col3 = st.columns(3)
 
 with col1:
-    st.subheader("溶剂参数")
+    st.subheader(lang["solvent_params"])
     df_params = pd.DataFrame({
-        "溶剂": [solvent_a_name, solvent_b_name],
-        "摩尔质量 (g/mol)": [M_a, M_b],
-        "密度 (g/cm³)": [rho_a, rho_b]
+        lang["solvent"]: [solvent_a_name, solvent_b_name],
+        f"{lang['molar_mass']} (g/mol)": [M_a, M_b],
+        f"{lang['density']} (g/cm³)": [rho_a, rho_b]
     })
     st.dataframe(df_params)
 
 with col2:
-    if conversion_mode == "摩尔分数 → 体积分数":
-        st.subheader("摩尔分数")
+    if conversion_mode == lang["mode_mole_to_vol"]:
+        st.subheader(lang["mole_fraction"])
         df_mole = pd.DataFrame({
-            "溶剂": [solvent_a_name, solvent_b_name],
-            "摩尔分数": [x_a, x_b]
+            lang["solvent"]: [solvent_a_name, solvent_b_name],
+            lang["mole_fraction"]: [x_a, x_b]
         })
         st.dataframe(df_mole)
     else:
-        st.subheader("体积分数")
+        st.subheader(lang["volume_fraction"])
         df_vol = pd.DataFrame({
-            "溶剂": [solvent_a_name, solvent_b_name],
-            "体积分数": [phi_a, phi_b]
+            lang["solvent"]: [solvent_a_name, solvent_b_name],
+            lang["volume_fraction"]: [phi_a, phi_b]
         })
         st.dataframe(df_vol)
 
 with col3:
-    if conversion_mode == "摩尔分数 → 体积分数":
-        st.subheader("体积分数")
+    if conversion_mode == lang["mode_mole_to_vol"]:
+        st.subheader(lang["volume_fraction"])
         df_vol_result = pd.DataFrame({
-            "溶剂": [solvent_a_name, solvent_b_name],
-            "体积分数": [phi_a, phi_b]
+            lang["solvent"]: [solvent_a_name, solvent_b_name],
+            lang["volume_fraction"]: [phi_a, phi_b]
         })
         st.dataframe(df_vol_result)
     else:
-        st.subheader("摩尔分数")
+        st.subheader(lang["mole_fraction"])
         df_mole_result = pd.DataFrame({
-            "溶剂": [solvent_a_name, solvent_b_name],
-            "摩尔分数": [x_a, x_b]
+            lang["solvent"]: [solvent_a_name, solvent_b_name],
+            lang["mole_fraction"]: [x_a, x_b]
         })
         st.dataframe(df_mole_result)
 
 # 公式说明
 st.markdown("---")
-st.header("计算公式")
-
-if conversion_mode == "摩尔分数 → 体积分数":
-    st.markdown("""
-    **摩尔分数转换为体积分数:**
-    
-    $$\\phi_A = \\frac{x_A \\cdot M_A / \\rho_A}{x_A \\cdot M_A / \\rho_A + x_B \\cdot M_B / \\rho_B}$$
-    
-    $$\\phi_B = \\frac{x_B \\cdot M_B / \\rho_B}{x_A \\cdot M_A / \\rho_A + x_B \\cdot M_B / \\rho_B}$$
-    
-    其中:
-    - $x_A, x_B$: 摩尔分数
-    - $\\phi_A, \\phi_B$: 体积分数
-    - $M_A, M_B$: 摩尔质量 (g/mol)
-    - $\\rho_A, \\rho_B$: 密度 (g/cm³)
-    """)
+st.header(lang["calculation_formula"])
+
+if conversion_mode == lang["mode_mole_to_vol"]:
+    if language == "中文":
+        st.markdown(f"""
+        {lang["formula_mole_to_vol_title"]}
+        
+        $$\\phi_A = \\frac{{x_A \\cdot M_A / \\rho_A}}{{x_A \\cdot M_A / \\rho_A + x_B \\cdot M_B / \\rho_B}}$$
+        
+        $$\\phi_B = \\frac{{x_B \\cdot M_B / \\rho_B}}{{x_A \\cdot M_A / \\rho_A + x_B \\cdot M_B / \\rho_B}}$$
+        
+        {lang["formula_where"]}
+        - $x_A, x_B$: 摩尔分数
+        - $\\phi_A, \\phi_B$: 体积分数
+        - $M_A, M_B$: 摩尔质量 (g/mol)
+        - $\\rho_A, \\rho_B$: 密度 (g/cm³)
+        """)
+    else:
+        st.markdown(f"""
+        {lang["formula_mole_to_vol_title"]}
+        
+        $$\\phi_A = \\frac{{x_A \\cdot M_A / \\rho_A}}{{x_A \\cdot M_A / \\rho_A + x_B \\cdot M_B / \\rho_B}}$$
+        
+        $$\\phi_B = \\frac{{x_B \\cdot M_B / \\rho_B}}{{x_A \\cdot M_A / \\rho_A + x_B \\cdot M_B / \\rho_B}}$$
+        
+        {lang["formula_where"]}
+        - $x_A, x_B$: Mole fractions
+        - $\\phi_A, \\phi_B$: Volume fractions
+        - $M_A, M_B$: Molar mass (g/mol)
+        - $\\rho_A, \\rho_B$: Density (g/cm³)
+        """)
 else:
-    st.markdown("""
-    **体积分数转换为摩尔分数:**
-    
-    $$x_A = \\frac{\\phi_A \\cdot \\rho_A / M_A}{\\phi_A \\cdot \\rho_A / M_A + \\phi_B \\cdot \\rho_B / M_B}$$
-    
-    $$x_B = \\frac{\\phi_B \\cdot \\rho_B / M_B}{\\phi_A \\cdot \\rho_A / M_A + \\phi_B \\cdot \\rho_B / M_B}$$
-    
-    其中:
-    - $\\phi_A, \\phi_B$: 体积分数
-    - $x_A, x_B$: 摩尔分数
-    - $M_A, M_B$: 摩尔质量 (g/mol)
-    - $\\rho_A, \\rho_B$: 密度 (g/cm³)
-    """)
+    if language == "中文":
+        st.markdown(f"""
+        {lang["formula_vol_to_mole_title"]}
+        
+        $$x_A = \\frac{{\\phi_A \\cdot \\rho_A / M_A}}{{\\phi_A \\cdot \\rho_A / M_A + \\phi_B \\cdot \\rho_B / M_B}}$$
+        
+        $$x_B = \\frac{{\\phi_B \\cdot \\rho_B / M_B}}{{\\phi_A \\cdot \\rho_A / M_A + \\phi_B \\cdot \\rho_B / M_B}}$$
+        
+        {lang["formula_where"]}
+        - $\\phi_A, \\phi_B$: 体积分数
+        - $x_A, x_B$: 摩尔分数
+        - $M_A, M_B$: 摩尔质量 (g/mol)
+        - $\\rho_A, \\rho_B$: 密度 (g/cm³)
+        """)
+    else:
+        st.markdown(f"""
+        {lang["formula_vol_to_mole_title"]}
+        
+        $$x_A = \\frac{{\\phi_A \\cdot \\rho_A / M_A}}{{\\phi_A \\cdot \\rho_A / M_A + \\phi_B \\cdot \\rho_B / M_B}}$$
+        
+        $$x_B = \\frac{{\\phi_B \\cdot \\rho_B / M_B}}{{\\phi_A \\cdot \\rho_A / M_A + \\phi_B \\cdot \\rho_B / M_B}}$$
+        
+        {lang["formula_where"]}
+        - $\\phi_A, \\phi_B$: Volume fractions
+        - $x_A, x_B$: Mole fractions
+        - $M_A, M_B$: Molar mass (g/mol)
+        - $\\rho_A, \\rho_B$: Density (g/cm³)
+        """)
 
 # 使用说明
 st.markdown("---")
-st.header("使用说明")
-st.markdown("""
-1. **选择转换模式**: 在侧边栏选择转换方向
-2. **选择溶剂**: 从预设的常见溶剂中选择，或选择"自定义"输入参数
-3. **输入数值**: 使用滑块调整摩尔分数或体积分数
-4. **查看结果**: 右侧显示转换结果和详细信息
-
-**注意**: 本计算假设理想混合，实际情况可能存在偏差。
+st.header(lang["usage_instructions"])
+st.markdown(f"""
+{lang["instruction_1"]}
+{lang["instruction_2"]}
+{lang["instruction_3"]}
+{lang["instruction_4"]}
+
+{lang["note"]}
 """)