Update src/streamlit_app.py

src/streamlit_app.py

@@ -6,10 +6,14 @@ import math
 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",
+        "main_title": "🧪 溶剂摩尔分数、体积分数与质量分数转换器",
         "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",
+        "mode_mole_to_mass": "摩尔分数 → 质量分数",
+        "mode_mass_to_mole": "质量分数 → 摩尔分数",
+        "mode_vol_to_mass": "体积分数 → 质量分数",
+        "mode_mass_to_vol": "质量分数 → 体积分数",
         "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:",
@@ -20,34 +24,46 @@ LANGUAGES = {
         "density": "密度",
         "input_mole_fraction": "输入摩尔分数",
         "input_volume_fraction": "输入体积分数",
+        "input_mass_fraction": "输入质量分数",
         "mole_fraction_of": "摩尔分数",
         "volume_fraction_of": "体积分数",
+        "mass_fraction_of": "质量分数",
         "result_volume_fraction": "计算结果 - 体积分数",
         "result_mole_fraction": "计算结果 - 摩尔分数",
+        "result_mass_fraction": "计算结果 - 质量分数",
         "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",
+        "mass_fraction": "质量分数",
         "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_mole_to_mass_title": "**摩尔分数转换为质量分数:**",
+        "formula_mass_to_mole_title": "**质量分数转换为摩尔分数:**",
+        "formula_vol_to_mass_title": "**体积分数转换为质量分数:**",
+        "formula_mass_to_vol_title": "**质量分数转换为体积分数:**",
         "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_3": "3. **输入数值**: 输入摩尔分数、体积分数或质量分数",
         "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",
+        "main_title": "🧪 Solvent Mole Fraction, Volume Fraction & Mass Fraction Converter",
         "conversion_mode": "Conversion Mode",
         "mode_mole_to_vol": "Mole Fraction → Volume Fraction",
         "mode_vol_to_mole": "Volume Fraction → Mole Fraction",
+        "mode_mole_to_mass": "Mole Fraction → Mass Fraction",
+        "mode_mass_to_mole": "Mass Fraction → Mole Fraction",
+        "mode_vol_to_mass": "Volume Fraction → Mass Fraction",
+        "mode_mass_to_vol": "Mass Fraction → Volume Fraction",
         "select_conversion": "Select conversion direction:",
         "solvent_selection": "Solvent Selection",
         "select_solvents": "Select two solvents or customize parameters:",
@@ -58,24 +74,32 @@ LANGUAGES = {
         "density": "Density",
         "input_mole_fraction": "Input Mole Fraction",
         "input_volume_fraction": "Input Volume Fraction",
+        "input_mass_fraction": "Input Mass Fraction",
         "mole_fraction_of": "Mole fraction of",
         "volume_fraction_of": "Volume fraction of",
+        "mass_fraction_of": "Mass fraction of",
         "result_volume_fraction": "Results - Volume Fraction",
         "result_mole_fraction": "Results - Mole Fraction",
+        "result_mass_fraction": "Results - Mass Fraction",
         "verification": "Verification",
         "detailed_info": "Detailed Information",
         "solvent_params": "Solvent Parameters",
         "solvent": "Solvent",
         "mole_fraction": "Mole Fraction",
         "volume_fraction": "Volume Fraction",
+        "mass_fraction": "Mass 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_mole_to_mass_title": "**Mole Fraction to Mass Fraction:**",
+        "formula_mass_to_mole_title": "**Mass Fraction to Mole Fraction:**",
+        "formula_vol_to_mass_title": "**Volume Fraction to Mass Fraction:**",
+        "formula_mass_to_vol_title": "**Mass Fraction to Volume 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_3": "3. **Input Values**: Input mole fraction, volume fraction or mass 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"
@@ -145,7 +169,9 @@ st.markdown("---")
 st.sidebar.header(lang["conversion_mode"])
 conversion_mode = st.sidebar.radio(
     lang["select_conversion"],
-    [lang["mode_mole_to_vol"], lang["mode_vol_to_mole"]]
+    [lang["mode_mole_to_vol"], lang["mode_vol_to_mole"], 
+     lang["mode_mole_to_mass"], lang["mode_mass_to_mole"],
+     lang["mode_vol_to_mass"], lang["mode_mass_to_vol"]]
 )
 
 # 溶剂选择
@@ -189,6 +215,7 @@ else:
 # 主界面内容
 col1, col2 = st.columns(2)
 
+# 摩尔分数 → 体积分数
 if conversion_mode == lang["mode_mole_to_vol"]:
     with col1:
         st.header(lang["input_mole_fraction"])
@@ -218,11 +245,10 @@ if conversion_mode == lang["mode_mole_to_vol"]:
         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"{lang['verification']}: φ_A + φ_B = {phi_a + phi_b:.4f}")
 
-else:  # 体积分数 → 摩尔分数
+# 体积分数 → 摩尔分数
+elif conversion_mode == lang["mode_vol_to_mole"]:
     with col1:
         st.header(lang["input_volume_fraction"])
         phi_a = st.number_input(
@@ -251,10 +277,136 @@ else:  # 体积分数 → 摩尔分数
         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}")
+        st.write(f"{lang['verification']}: x_A + x_B = {x_a + x_b:.4f}")
+
+# 摩尔分数 → 质量分数
+elif conversion_mode == lang["mode_mole_to_mass"]:
+    with col1:
+        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=0.001,
+            format="%.4f"
+        )
+        x_b = 1.0 - x_a
+        st.write(f"{lang['mole_fraction_of']} {solvent_b_name} (x_B): {x_b:.4f}")
+        
+        # 计算质量分数
+        mass_a = x_a * M_a
+        mass_b = x_b * M_b
+        mass_total = mass_a + mass_b
+        
+        if mass_total > 0:
+            w_a = mass_a / mass_total
+            w_b = mass_b / mass_total
+        else:
+            w_a = w_b = 0
         
-        # 验证
+    with col2:
+        st.header(lang["result_mass_fraction"])
+        st.metric(f"{lang['mass_fraction_of']} {solvent_a_name} (w_A)", f"{w_a:.4f}")
+        st.metric(f"{lang['mass_fraction_of']} {solvent_b_name} (w_B)", f"{w_b:.4f}")
+        st.write(f"{lang['verification']}: w_A + w_B = {w_a + w_b:.4f}")
+
+# 质量分数 → 摩尔分数
+elif conversion_mode == lang["mode_mass_to_mole"]:
+    with col1:
+        st.header(lang["input_mass_fraction"])
+        w_a = st.number_input(
+            f"{lang['mass_fraction_of']} {solvent_a_name} (w_A):",
+            min_value=0.0,
+            max_value=1.0,
+            value=0.5,
+            step=0.001,
+            format="%.4f"
+        )
+        w_b = 1.0 - w_a
+        st.write(f"{lang['mass_fraction_of']} {solvent_b_name} (w_B): {w_b:.4f}")
+        
+        # 计算摩尔分数
+        n_ratio_a = w_a / M_a
+        n_ratio_b = w_b / M_b
+        n_total = n_ratio_a + n_ratio_b
+        
+        if n_total > 0:
+            x_a = n_ratio_a / n_total
+            x_b = n_ratio_b / n_total
+        else:
+            x_a = x_b = 0
+        
+    with col2:
+        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}")
         st.write(f"{lang['verification']}: x_A + x_B = {x_a + x_b:.4f}")
 
+# 体积分数 → 质量分数
+elif conversion_mode == lang["mode_vol_to_mass"]:
+    with col1:
+        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=0.001,
+            format="%.4f"
+        )
+        phi_b = 1.0 - phi_a
+        st.write(f"{lang['volume_fraction_of']} {solvent_b_name} (φ_B): {phi_b:.4f}")
+        
+        # 计算质量分数
+        mass_a = phi_a * rho_a
+        mass_b = phi_b * rho_b
+        mass_total = mass_a + mass_b
+        
+        if mass_total > 0:
+            w_a = mass_a / mass_total
+            w_b = mass_b / mass_total
+        else:
+            w_a = w_b = 0
+        
+    with col2:
+        st.header(lang["result_mass_fraction"])
+        st.metric(f"{lang['mass_fraction_of']} {solvent_a_name} (w_A)", f"{w_a:.4f}")
+        st.metric(f"{lang['mass_fraction_of']} {solvent_b_name} (w_B)", f"{w_b:.4f}")
+        st.write(f"{lang['verification']}: w_A + w_B = {w_a + w_b:.4f}")
+
+# 质量分数 → 体积分数
+elif conversion_mode == lang["mode_mass_to_vol"]:
+    with col1:
+        st.header(lang["input_mass_fraction"])
+        w_a = st.number_input(
+            f"{lang['mass_fraction_of']} {solvent_a_name} (w_A):",
+            min_value=0.0,
+            max_value=1.0,
+            value=0.5,
+            step=0.001,
+            format="%.4f"
+        )
+        w_b = 1.0 - w_a
+        st.write(f"{lang['mass_fraction_of']} {solvent_b_name} (w_B): {w_b:.4f}")
+        
+        # 计算体积分数
+        vol_a = w_a / rho_a
+        vol_b = w_b / rho_b
+        vol_total = vol_a + vol_b
+        
+        if vol_total > 0:
+            phi_a = vol_a / vol_total
+            phi_b = vol_b / vol_total
+        else:
+            phi_a = phi_b = 0
+        
+    with col2:
+        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}")
+        st.write(f"{lang['verification']}: φ_A + φ_B = {phi_a + phi_b:.4f}")
+
 # 详细信息展示
 st.markdown("---")
 st.header(lang["detailed_info"])
@@ -271,36 +423,95 @@ with col1:
     st.dataframe(df_params)
 
 with col2:
-    if conversion_mode == lang["mode_mole_to_vol"]:
-        st.subheader(lang["mole_fraction"])
-        df_mole = pd.DataFrame({
-            lang["solvent"]: [solvent_a_name, solvent_b_name],
-            lang["mole_fraction"]: [x_a, x_b]
-        })
-        st.dataframe(df_mole)
-    else:
-        st.subheader(lang["volume_fraction"])
-        df_vol = pd.DataFrame({
-            lang["solvent"]: [solvent_a_name, solvent_b_name],
-            lang["volume_fraction"]: [phi_a, phi_b]
-        })
-        st.dataframe(df_vol)
+    if "mole" in conversion_mode:
+        if conversion_mode in [lang["mode_mole_to_vol"], lang["mode_mole_to_mass"]]:
+            st.subheader(lang["mole_fraction"])
+            df_input = pd.DataFrame({
+                lang["solvent"]: [solvent_a_name, solvent_b_name],
+                lang["mole_fraction"]: [x_a, x_b]
+            })
+            st.dataframe(df_input)
+        else:
+            st.subheader(lang["mole_fraction"])
+            df_result = pd.DataFrame({
+                lang["solvent"]: [solvent_a_name, solvent_b_name],
+                lang["mole_fraction"]: [x_a, x_b]
+            })
+            st.dataframe(df_result)
+    elif "vol" in conversion_mode:
+        if conversion_mode in [lang["mode_vol_to_mole"], lang["mode_vol_to_mass"]]:
+            st.subheader(lang["volume_fraction"])
+            df_input = pd.DataFrame({
+                lang["solvent"]: [solvent_a_name, solvent_b_name],
+                lang["volume_fraction"]: [phi_a, phi_b]
+            })
+            st.dataframe(df_input)
+        else:
+            st.subheader(lang["volume_fraction"])
+            df_result = pd.DataFrame({
+                lang["solvent"]: [solvent_a_name, solvent_b_name],
+                lang["volume_fraction"]: [phi_a, phi_b]
+            })
+            st.dataframe(df_result)
+    elif "mass" in conversion_mode:
+        if conversion_mode in [lang["mode_mass_to_mole"], lang["mode_mass_to_vol"]]:
+            st.subheader(lang["mass_fraction"])
+            df_input = pd.DataFrame({
+                lang["solvent"]: [solvent_a_name, solvent_b_name],
+                lang["mass_fraction"]: [w_a, w_b]
+            })
+            st.dataframe(df_input)
+        else:
+            st.subheader(lang["mass_fraction"])
+            df_result = pd.DataFrame({
+                lang["solvent"]: [solvent_a_name, solvent_b_name],
+                lang["mass_fraction"]: [w_a, w_b]
+            })
+            st.dataframe(df_result)
 
 with col3:
     if conversion_mode == lang["mode_mole_to_vol"]:
         st.subheader(lang["volume_fraction"])
-        df_vol_result = pd.DataFrame({
+        df_result = pd.DataFrame({
             lang["solvent"]: [solvent_a_name, solvent_b_name],
             lang["volume_fraction"]: [phi_a, phi_b]
         })
-        st.dataframe(df_vol_result)
-    else:
+        st.dataframe(df_result)
+    elif conversion_mode == lang["mode_mole_to_mass"]:
+        st.subheader(lang["mass_fraction"])
+        df_result = pd.DataFrame({
+            lang["solvent"]: [solvent_a_name, solvent_b_name],
+            lang["mass_fraction"]: [w_a, w_b]
+        })
+        st.dataframe(df_result)
+    elif conversion_mode == lang["mode_vol_to_mole"]:
+        st.subheader(lang["mole_fraction"])
+        df_result = pd.DataFrame({
+            lang["solvent"]: [solvent_a_name, solvent_b_name],
+            lang["mole_fraction"]: [x_a, x_b]
+        })
+        st.dataframe(df_result)
+    elif conversion_mode == lang["mode_vol_to_mass"]:
+        st.subheader(lang["mass_fraction"])
+        df_result = pd.DataFrame({
+            lang["solvent"]: [solvent_a_name, solvent_b_name],
+            lang["mass_fraction"]: [w_a, w_b]
+        })
+        st.dataframe(df_result)
+    elif conversion_mode == lang["mode_mass_to_mole"]:
         st.subheader(lang["mole_fraction"])
-        df_mole_result = pd.DataFrame({
+        df_result = pd.DataFrame({
             lang["solvent"]: [solvent_a_name, solvent_b_name],
             lang["mole_fraction"]: [x_a, x_b]
         })
-        st.dataframe(df_mole_result)
+        st.dataframe(df_result)
+    elif conversion_mode == lang["mode_mass_to_vol"]:
+        st.subheader(lang["volume_fraction"])
+        df_result = pd.DataFrame({
+            lang["solvent"]: [solvent_a_name, solvent_b_name],
+            lang["volume_fraction"]: [phi_a, phi_b]
+        })
+        st.dataframe(df_result)
 
 # 公式说明
 st.markdown("---")
@@ -313,8 +524,6 @@ if conversion_mode == lang["mode_mole_to_vol"]:
         
         $$\\phi_A = \\frac{{x_A \\cdot M_A / \\rho_A}}{{x_A \\cdot M_A / \\rho_A + x_B \\cdot M_B / \\rho_B}}$$
         
-        $$\\phi_B = \\frac{{x_B \\cdot M_B / \\rho_B}}{{x_A \\cdot M_A / \\rho_A + x_B \\cdot M_B / \\rho_B}}$$
-        
         {lang["formula_where"]}
         - $x_A, x_B$: 摩尔分数
         - $\\phi_A, \\phi_B$: 体积分数
@@ -327,23 +536,20 @@ if conversion_mode == lang["mode_mole_to_vol"]:
         
         $$\\phi_A = \\frac{{x_A \\cdot M_A / \\rho_A}}{{x_A \\cdot M_A / \\rho_A + x_B \\cdot M_B / \\rho_B}}$$
         
-        $$\\phi_B = \\frac{{x_B \\cdot M_B / \\rho_B}}{{x_A \\cdot M_A / \\rho_A + x_B \\cdot M_B / \\rho_B}}$$
-        
         {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:
+
+elif conversion_mode == lang["mode_vol_to_mole"]:
     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
@@ -356,8 +562,6 @@ else:
         
         $$x_A = \\frac{{\\phi_A \\cdot \\rho_A / M_A}}{{\\phi_A \\cdot \\rho_A / M_A + \\phi_B \\cdot \\rho_B / M_B}}$$
         
-        $$x_B = \\frac{{\\phi_B \\cdot \\rho_B / M_B}}{{\\phi_A \\cdot \\rho_A / M_A + \\phi_B \\cdot \\rho_B / M_B}}$$
-        
         {lang["formula_where"]}
         - $\\phi_A, \\phi_B$: Volume fractions
         - $x_A, x_B$: Mole fractions
@@ -365,6 +569,102 @@ else:
         - $\\rho_A, \\rho_B$: Density (g/cm³)
         """)
 
+elif conversion_mode == lang["mode_mole_to_mass"]:
+    if language == "中文":
+        st.markdown(f"""
+        {lang["formula_mole_to_mass_title"]}
+        
+        $$w_A = \\frac{{x_A \\cdot M_A}}{{x_A \\cdot M_A + x_B \\cdot M_B}}$$
+        
+        {lang["formula_where"]}
+        - $x_A, x_B$: 摩尔分数
+        - $w_A, w_B$: 质量分数
+        - $M_A, M_B$: 摩尔质量 (g/mol)
+        """)
+    else:
+        st.markdown(f"""
+        {lang["formula_mole_to_mass_title"]}
+        
+        $$w_A = \\frac{{x_A \\cdot M_A}}{{x_A \\cdot M_A + x_B \\cdot M_B}}$$
+        
+        {lang["formula_where"]}
+        - $x_A, x_B$: Mole fractions
+        - $w_A, w_B$: Mass fractions
+        - $M_A, M_B$: Molar mass (g/mol)
+        """)
+
+elif conversion_mode == lang["mode_mass_to_mole"]:
+    if language == "中文":
+        st.markdown(f"""
+        {lang["formula_mass_to_mole_title"]}
+        
+        $$x_A = \\frac{{w_A / M_A}}{{w_A / M_A + w_B / M_B}}$$
+        
+        {lang["formula_where"]}
+        - $w_A, w_B$: 质量分数
+        - $x_A, x_B$: 摩尔分数
+        - $M_A, M_B$: 摩尔质量 (g/mol)
+        """)
+    else:
+        st.markdown(f"""
+        {lang["formula_mass_to_mole_title"]}
+        
+        $$x_A = \\frac{{w_A / M_A}}{{w_A / M_A + w_B / M_B}}$$
+        
+        {lang["formula_where"]}
+        - $w_A, w_B$: Mass fractions
+        - $x_A, x_B$: Mole fractions
+        - $M_A, M_B$: Molar mass (g/mol)
+        """)
+
+elif conversion_mode == lang["mode_vol_to_mass"]:
+    if language == "中文":
+        st.markdown(f"""
+        {lang["formula_vol_to_mass_title"]}
+        
+        $$w_A = \\frac{{\\phi_A \\cdot \\rho_A}}{{\\phi_A \\cdot \\rho_A + \\phi_B \\cdot \\rho_B}}$$
+        
+        {lang["formula_where"]}
+        - $\\phi_A, \\phi_B$: 体积分数
+        - $w_A, w_B$: 质量分数
+        - $\\rho_A, \\rho_B$: 密度 (g/cm³)
+        """)
+    else:
+        st.markdown(f"""
+        {lang["formula_vol_to_mass_title"]}
+        
+        $$w_A = \\frac{{\\phi_A \\cdot \\rho_A}}{{\\phi_A \\cdot \\rho_A + \\phi_B \\cdot \\rho_B}}$$
+        
+        {lang["formula_where"]}
+        - $\\phi_A, \\phi_B$: Volume fractions
+        - $w_A, w_B$: Mass fractions
+        - $\\rho_A, \\rho_B$: Density (g/cm³)
+        """)
+
+elif conversion_mode == lang["mode_mass_to_vol"]:
+    if language == "中文":
+        st.markdown(f"""
+        {lang["formula_mass_to_vol_title"]}
+        
+        $$\\phi_A = \\frac{{w_A / \\rho_A}}{{w_A / \\rho_A + w_B / \\rho_B}}$$
+        
+        {lang["formula_where"]}
+        - $w_A, w_B$: 质量分数
+        - $\\phi_A, \\phi_B$: 体积分数
+        - $\\rho_A, \\rho_B$: 密度 (g/cm³)
+        """)
+    else:
+        st.markdown(f"""
+        {lang["formula_mass_to_vol_title"]}
+        
+        $$\\phi_A = \\frac{{w_A / \\rho_A}}{{w_A / \\rho_A + w_B / \\rho_B}}$$
+        
+        {lang["formula_where"]}
+        - $w_A, w_B$: Mass fractions
+        - $\\phi_A, \\phi_B$: Volume fractions
+        - $\\rho_A, \\rho_B$: Density (g/cm³)
+        """)
+
 # 使用说明
 st.markdown("---")
 st.header(lang["usage_instructions"])